Fairness Ideals in Distribution Channels

Abstract

The authors analytically and experimentally evaluate how firms make decisions in a two-stage dyadic channel, in which firms decide on investments in the first stage and then on prices in the second stage. They find that firms’ behavior differs significantly from the predictions of the standard economic model and is consistent with the existence of fairness concerns. Using a quantal response equilibrium model, in which both manufacturer and retailer make noisy best responses, the authors show that fairness significantly affects channel pricing decisions. In addition, they investigate what affects the perceptions of fairness. More specifically, they analyze whether the notion of fairness is influenced by social norms of strict equality, by endogenous investments and contributions that are affected by players’ decisions, or by the exogenous game structure. To do so, the authors compare four principles of distributive fairness: strict egalitarianism; liberal egalitarianism; libertarianism; and a sequence-aligned ideal, which is studied for the first time in the literature. Surprisingly, the exogenous game structure reflected by the new ideal, whereby the sequence of moving determines the equitable payoff for players, significantly outperforms other fairness ideals, suggesting that equity in distribution channels can arise even in contests in which channel members have fairly different payoffs.

Keywords

fairness ideals distribution channels quantal response equilibrium experimental economics

Research in behavioral and experimental economics has suggested that concerns for fairness affect a wide range of agents’ behaviors.¹ Participants in various versions of the ultimatum and dictator games routinely offer higher-than-optimal shares of the initial endowment, and responders virtually always turn down low offers that are significantly higher than predicted by standard economic models (Camerer 2003).

Researchers have also surveyed consumers and companies to investigate what is considered fair in circumstances ranging from price increases to renting contracts, and they have found that people largely agree on what is fair and what is not fair, suggesting that fairness is a widely understood concept (Anderson and Simester 2004, 2008, 2010; Bolton, Warlop, and Alba 2003; Güth, Schmittberger, and Schwarze 1982; Kahneman, Knetsch, and Thaler 1986a, b). In addition, empirical evidence has indicated that fairness/equity plays an important role in certain business contexts (e.g., Heide and John 1992; Jap 2001; Jap and Anderson 2003; Kumar, Scheer, and Steenkamp 1995; Olmstead and Rhode 1985; Scheer, Kumar, and Steenkamp 2003, Zaheer, McEvily, and Perrone 1998, Zaheer and Venkatraman 1995). For instance, in a study surveying 417 U.S. auto dealers and 289 Dutch auto dealers, Scheer, Kumar, and Steenkamp (2003) find that auto dealers have concerns for distributive fairness with their business partners. Furthermore, they also find that inequity plays a very different role for dealers across cultures, with U.S. dealers reacting only to disadvantageous inequity and Dutch dealers reacting to both disadvantageous and advantageous inequity.

There is also strong experimental support for fairness concerns from contracting agents (Fehr, Klein, and Schmidt 2007; Hackett 1994; Ho and Su 2009; Loch and Wu 2008). For example, Fehr, Klein, and Schmidt (2007) show that bonus contracts that offer a voluntary and unenforceable bonus for satisfactory performance provide powerful incentives and are superior to explicit incentive contracts when there are some fair-minded players. There is also ample evidence in neuroscience and psychology research suggesting that human decision makers have intrinsic concerns for fairness (Bechara and Damasio 2005; Koenigs et al. 2007; Sanfey et al. 2003; Stephen and Pham 2008). Stephen and Pham (2008), for instance, find that decision makers’ feelings of fairness and emotions play an important role in ultimatum games and negotiations.

Given the widely documented importance of fairness in various business contexts, surprisingly few models of channel incorporate fairness concerns in the utility functions of retailers or manufacturers. Among the few exceptions, Cui, Raju, and Zhang (2007) model the effect of fairness concerns on the interactions between the manufacturer and the retailer in a dyadic channel with linear demand. They demonstrate that the manufacturer can use a single wholesale price to coordinate the channel as long as the retailer has strong concerns for fairness. That is, the double marginalization problem can be avoided in such a fair channel. Caliskan-Demirag, Chen, and Li (2010) extend Cui, Raju, and Zhang to consider nonlinear demand functions and find that a linear wholesale price can coordinate the channel at a wider range when the retailer is fair-minded. Pavlov and Katok (2011) find that a linear pricing contract can still maximize the channel profit even when there is information asymmetry between channel members about fairness concerns. Given that many empirical research studies have documented and analyzed the importance of fairness to a healthy relationship between channel members,² why are more researchers not incorporating fairness in their models of channel behavior? In an elegant recent study, Ho, Su, and Wu (2014) investigate how two types of fairness concerns, distributive fairness and peer-induced fairness, between one supplier and two peer retailers may influence the economic outcomes in such a channel. They find that both the wholesale price and the firms’ profits are significantly influenced by fairness concerns in the channel.

Even if fairness concerns exist in channels, ignoring them in models might not be a big issue if such concerns are relatively marginal compared with other motives, such as the profit-maximizing motive. Indeed, the vast majority of studies that establish the existence of fairness are run in simplified contexts (typically dictator and ultimatum games), in which the profit-maximization problem is relatively simple. In contrast, the profit-maximization problem in channels is quite complex, requiring advanced strategic thinking and computational capabilities. Thus, in such a complex context, it might be reasonable to expect that fairness concerns will play a marginal role, subordinated to the concerns for profit maximization. In this case, modelers might have a good reason to ignore fairness concerns.

One of our research goals is to establish whether fairness is an important concern that should be incorporated in models along with the profit motive or a marginal concern that can be safely ignored. We experimentally investigate pricing decisions in a dyadic channel in which the manufacturer acts as a Stackelberg leader in choosing prices and the retailer acts as a follower, and we build a quantal response equilibrium (QRE) model (McKelvey and Palfrey 1995) that incorporates the retailer's concerns for fairness, bounded rationality, and profit motives by firms to explain the discrepancy between the theoretical predictions and empirical regularities. We chose such a game setup because decision makers’ behaviors in a complex distribution channel may be affected by many factors such as multiple decisions, response uncertainty, bounded rationality, and an indirect link between firms’ investments and payoffs. Most of these factors are not present in simple games that are commonly used to study fairness (e.g., the ultimatum game, the dictator game). It is important to examine whether fairness concerns still exist in such a complicated system and whether such concerns can significantly influence managers’ behaviors and channel efficiency. Thus, by estimating such an enriched model, we are able to investigate whether fairness concerns are managerially relevant in the channel context and how they compare with profit motives. As such, our experimental investigation of the channel context enables us to estimate and compare fairness concerns with profit-maximization motives. This research approach also contrasts with the approach of some previous studies, which have shown the existence of fairness concerns in channels but could not directly compare the importance of such concerns with the importance of the concerns for profit. We find that fairness not only is present in channels but also can be quite strong compared with profit motives.

Similarly, fairness might not matter much compared with the profit-maximization motive if the decision makers are sophisticated agents who care less about fairness than about profit maximization relative to the average experimental participants. In our study, we examine and contrast the behaviors of a less sophisticated population (undergraduate students) with a more experienced population (master of business administration [MBA] students).³ We find evidence that the MBA population is indeed more sophisticated and that the MBA participants tend to make fewer mistakes than their undergraduate counterparts, but we find no substantial difference in their concerns for fairness. If anything, the MBA population seems more concerned with fairness than their undergraduate counterparts.

Another open question in the fairness literature is how channel members determine what a fair outcome is. In particular, is a fair split of profit determined by endogenous factors that are under channel members’ control (e.g., investments in the channel) or by exogenous factors that are not under their control (e.g., the role of the player, the structure of the game)? This question is particularly interesting because in the first instance, participants can influence their utility by manipulating the fair outcome, whereas in the second instance, they have no control over the fair outcome.

To determine what factors affect channel members’ fair outcomes, we compare four fairness principles: strict egalitarianism, liberal egalitarianism, libertarianism (Cappelen et al. 2007), and a new principle of fairness we propose—the sequence-aligned ideal. The strict egalitarian ideal refers to the social norm of strict equality. The liberal egalitarian ideal and the libertarian ideal are affected by the investments and contributions made by channel members to the channel and thus depend on the endogenous decisions of channel members. In contrast, the sequence-aligned ideal does not depend on endogenous subject decisions but rather depends only on the exogenous game structure. We find that the ideal with exogenous game structure fits our data better than any other ideals that capture either endogenous participant decisions or the norm of strict equality, suggesting that modelers and practitioners should be more concerned with exogenous factors such as game structure than endogenous factors when trying to understand the effect of fairness in a distribution channel. The newly proposed sequence-aligned principle of fairness reflects the game structure in the dyadic channel and proposes that the equitable payoff should be consistent with the ratio of players’ profits in the standard Stackelberg game. This new finding suggests that in the context of channel relations, it is perceived as “fair” for the manufacturer, acting as the Stackelberg leader in our model, to obtain a higher payoff than the retailer, acting as a follower. Our research is one of the first in the literature to empirically study what is considered a fair deal in pricing games in distribution channels (Ho, Su, and Wu 2014; Katok, Olsen, and Pavlov 2012).

This new fairness ideal underscores the notion that fairness and exogenous game structure are not at odds with each other. This is a departure from the area of the literature that argues that fairness and the roles of channel members are two distinct forces and that fairness, but not the roles of channel members, has a positive effect on channel relationships and can help improve channel profits (Kumar 1996; Kumar, Scheer, and Steenkamp 1995). Indeed, we find that under this new fairness ideal, optimal profits are higher than under the strict egalitarian ideal that ignores channel members’ roles uniquely determined by the game structure. Thus, fairness and game structure are not two distinct forces that affect channel dynamics separately. In contrast, they interact and the perception of fairness can be influenced by the exogenous factor of game structure.

In summary, we are able to make the following contributions. (1) We add to the literature on fairness and channels by showing not only that fairness concerns coexist with the profit-maximization motives but that the size of such concerns is comparable to the size of the profit-maximization motives, thereby underscoring the importance of including fairness in channel models. This result can be expanded to the fairness literature in general and can provide further evidence of the importance of fairness between contracting parties by suggesting that fairness is a relevant concern even in a complex context such as in a distribution channel. Such concerns do not disappear for sophisticated agents. (2) Exogenous factors such as the structure of the game and the roles of the players are more likely to affect the fair outcome than endogenous factors such as investments; in particular, a Stackelberg game results in a fair, but uneven, profit split between the two players, with the manufacturer, the leader in the game, “deserving” approximately twice as much as the retailer. (3) Fairness and game structure, far from being two separate and independent factors, can have quite a complex relationship. Indeed, we found that exogenous game structure seems to affect the perception of fairness and can also improve the profit-enhancing ability of fairness.

Our article is closely related to Cappelen et al. (2007), who studied three fairness ideals—strict egalitarianism, liberal egalitarianism, and libertarianism—in a dictator distribution game in which the outputs of a production stage may determine the equitable payoff. However, our research differs from Cappelen et al. in three important ways. (1) This article presents a behavioral model that incorporates both bounded rationality and fairness concerns, whereas Cappelen et al. consider only fairness concerns. This addition enables us to better distinguish between deviations from rational decisions due to participants’ mistakes and deviations due to concerns for fairness. (2) We propose a new fairness ideal, the sequence-aligned ideal, which is novel in the literature and generalizes the concept of strict egalitarianism. This ideal is particularly suited to the channel context because it captures the difference in channel members’ roles that are determined by the exogenously given game structure. Indeed, we show that the newly proposed fairness ideal outperforms other fairness ideals in our experimental studies. (3) In our article, players in a dyadic channel make pricing decisions in the second stage of the game, whereas in Cappelen et al., the dictator decides the amount of currency to give the passive receiver in the second stage. The active role of the retailer, who decides on retail price in the second stage of the game and can punish the manufacturer for unfair behaviors, not only provides a more realistic setting but also forces manufacturers to carefully consider retailers’ preferences and concerns about fairness. In addition, the setting in our article is more closely related to the dyadic channel structure that is widely studied in marketing.

Our research also contributes to the literature on incorporating behavioral theories into quantitative models to better understand how certain behavioral factors may affect firms’ decisions. This includes cognitive hierarchy (Camerer, Ho, and Chong 2004; Cui and Xiao 2016; Cui and Zhang 2016; Goldfarb and Xiao 2011; Goldfarb and Yang 2009; Ho and Su 2013), fairness concerns (Chen and Cui 2013; Cui, Mallucci, and Wu 2016; Cui, Raju, and Zhang 2007; Feinberg, Krishna, and Zhang 2002), bounded rationality (Che, Sudhir, and Seetharaman 2007; Chen, Iyer, and Pazgal 2010), loss and/or risk aversion (Hardie, Johnson, and Fader 1993; Ho, Lim, and Cui 2010; Kalra and Shi 2010; Zhang, Donohue, and Cui 2016), regret or counterfactual considerations (Lim and Ho 2007; Syam, Krishnamurthy, and Hess 2008), reference dependency (Amaldoss and Jain 2010; Cui, Raju, and Shi 2015; Ho and Zhang 2008; Orhun 2009), emotions (Sanfey et al. 2003; Stephen and Pham 2008), and learning (Amaldoss, Bettman, and Payne 2008; Amaldoss and Jain 2005; Bradlow, Hu, and Ho 2004a, b; Chen, Su, and Zhao 2012; Ho and Weigelt 1996).

The rest of this article is organized as follows. In the next section, we outline the standard economic model with theoretical predictions on prices and investments. Then, we introduce a behavioral model that incorporates bounded rationality and fairness concerns by channel members. In subsequent sections, we describe the experimental design and experimental studies, report the results of the estimated model, and formally test the theoretical predictions. We conclude with main findings from our analysis and directions for further research.

Standard Economic Model

In this section, we present the standard economic model. The standard economic model refers to the game theoretical model, in which decision makers are rational profit or utility maximizers (Amaldoss and Jain 2015; Ho, Lim, and Camerer 2006). Therefore, the model provides the theoretical predictions of the investments and prices that channel members choose when they maximize profits.

Consider the standard dyadic channel, in which a single manufacturer sells its product to consumers through a single retailer. There are two stages. Each firm has an initial endowment of E at the beginning of the first stage. In stage one, both manufacturer and retailer simultaneously decide on the amount of investment out of their initial endowment E that they would like to invest to increase the demand of the product. We denote I_M ≤ E as the manufacturer's investment and I_R ≤ E as the retailer's investment. Given their investments, the manufacturer moves first and charges a constant wholesale price w. Taking the wholesale price w as given, the retailer sets the retail price p. Without loss of generality, we assume that the production cost c is given by zero. The market demand is given by D(p) = BD – b × p = a + I_M × R_M + I_R × R_R – b × p, where BD = a + I_M × R_M + I_R × R_R refers to the base demand of the product, R_M > 0 (R_R > 0) represents the rate of return for the manufacturer's (retailer's) investment, and b > 0. We denote π_M = w × D(p) as the manufacturer's profit from sales of products and π_R = (p – w) × D(p) as the retailer's profit from sales of products. Thus, the manufacturer's total profit is given by ∏_M(I_M, w) = E – I_M + π_M = E – I_M + w × D(p) and the retailer's total profit is given by ∏_R(I_R, p) = E – I_R + π_R = E – I_R + (p – w) × D(p).

We solved the model using backward induction (for detailed proofs, see Web Appendix A⁴). We first solve the sequential pricing game given any investments by the manufacturer and retailer. Firms’ investments are then solved given firms’ price decisions as a function of firms’ investments. Given investments I_M and I_R, the optimal wholesale price is given by (I_M, I_R) = BD/2b = (a + I_MR_M + I_RR_R)/2b and the optimal retail price is given by p(I_M, I_R) = (3 × BD/4b) × [3(a + I_MR_M + I_RR_R)/4b] Given firms’ best-response prices and the other firm's investment, a firm's profit is a convex function of its investment, and the optimal investments are given by

(I_{M}^{*}, I_{R}^{*}) = {\begin{array}{l} (0, 0) & if 0 < R_{M} < R_{M 1} and 0 < R_{R} < R_{R1} \\ (0, E) & if 0 < R_{M} < R_{M2} {and R}_{R} \geq R_{R1} \\ (E, 0) & {if R}_{M} \geq R_{M 1} and 0 < R_{R} < R_{R2} \\ (E, E) & {if R}_{M} \geq R_{M2} {and R}_{R} \geq R_{R2} \end{array} .

(1)

The threshold values of return rates are defined as $R_{M 1} = (1 / E) (\sqrt{a^{2} + 8 bE} - a)$ , $R_{R 1} = (1 / E) (\sqrt{a^{2} + 16 bE} - a)$ and R_M2 and R_R2 simultaneously solved from $Φ_{M} (R_{M 2}, R_{R2}) = 0$ and $Φ_{R} (R_{M 2}, R_{R2}) = 0$ where the functions $Φ_{M}$ and $Φ_{R}$ are given by

{\begin{matrix} Φ_{M} (x, y) & = & E \times x^{2} + 2 (a + E \times y) x - 8 b \\ Φ_{R} (x, y) & = & E \times y^{2} + 2 (a + E \times x) y - 16 b \end{matrix} .

(2)

BEHAVIORAL MODEL WITH FAIRNESS AND BOUNDED RATIONALITY

In the standard economic model, decision makers are rational profit or utility maximizers. However, they may have concerns regarding fairness (Fehr and Schmidt 1999; Güth, Schmittberger, and Schwarze 1982; Ho and Su 2009). In addition to fairness concerns, another possible reason for players’ decisions to deviate from predictions of the standard economic model is bounded rationality; that is, players are trying to maximize profits but are making mistakes in their decisions at the same time. We generalize the standard economic model to incorporate both fairness concerns and bounded rationality. To identify the bounded rationality in our empirical estimation afterward, we employ the QRE model (Ho and Zhang 2008; Lim and Ho 2007; McKelvey and Palfrey 1995).

We begin with a discussion of the fairness ideals that determine the equitable payoff for a fair-minded firm. Next, we analyze the QRE model, which incorporates fairness concerns expressed by different fairness ideals. Finally, in subsequent sections, we estimate the QRE model with fairness concerns using the empirical data we collected in laboratory experiments.

Fairness Ideals

We use the model of distributive fairness (Fehr and Schmidt 1999) to conceptualize fairness concerns between channel members. A firm with concerns for distributive fairness experiences disutility from inequity in the allocation of payoffs. The negative effect of inequity is stronger when the firm has a lower payoff compared with its equitable payoff (i.e., when a disadvantageous inequality occurs) than when the firm has a higher payoff (i.e., when an advantageous inequality occurs). The equitable payoff is the amount of monetary payoff a firm considers a fair deal.

We follow Cui, Raju, and Zhang (2007) in assuming that the retailer in the channel displays concerns for fairness, whereas the manufacturer is a profit maximizer.⁵ The manufacturer's and retailer's payoffs from sales of product are denoted, respectively, as π_M and π_R, and the retailer's utility is given by

\begin{matrix} U_{R} & = Π_{R} - α \times max {\frac{τ}{1 - τ} π_{M} - π_{R}, 0} \\ - β \times max {π_{R} - \frac{τ}{1 - τ} π_{M}, 0}, \end{matrix}

(3)

for α ≥ β, and 0 < β < 1.⁶ The terms in parentheses are used to distinguish between advantageous and disadvantageous inequality. To represent an agent that is more adverse to disadvantageous inequality than advantageous inequality, it is further assumed that α ≥ β.

If participants care about fairness as measured by aversion to (dis)advantageous inequality, then their pricing decisions would be affected by their concerns for fairness. Thus, when we estimate the determinants of participants’ pricing decisions, we expect significant influences of aversion to (dis)advantageous inequality. This leads to the following hypotheses:

H_1a: If participants’ pricing decisions are affected by disadvanta-geous inequality, α is larger than zero.

H_1b: If participants’ pricing decisions are affected by advanta-geous inequality, β is larger than zero.

In the utility function, different values of τ/(1 - τ) represent different fairness ideals. The fairness ideal captures how a player's equitable payoff is determined. What players consider fair can vary as a result of exogenous environmental factors such as social norms and game structure, as well as endogenous factors such as the investments or contributions the players make in the game. Our experimental setup, in which the investments of different players affect both the base demand of the product and firms’ profits, is similar to an economy with investment-dependent market demands. In such a context, what is considered a fair profit allocation can depend on the concept we use to define fairness, the so-called “fairness ideal.” The three most prominent fairness ideals studied in literature thus far are strict libertarianism, strict egalitarianism, and liberal egalitarianism (Cappelen et al. 2007).

Strict egalitarianism claims that agents should get the same share of the final outcome, irrespective of their respective contributions. Thus, strict egalitarianism represents social norms of strict equality. Strict libertarianism argues that agents’ payoffs should be in agreement with their total contributions, including the endogenous factors under their control (i.e., investments) and the factors outside of their control (i.e., return rates on investments). Liberal egalitarianism takes a middle-ground position, arguing that agents’ final profits should be divided in proportion to the endogenous factors that are under their control (i.e., investments).

In addition, we propose a fourth fairness ideal, termed the “sequence-aligned ideal.” According to this ideal, the players’ payoff should be consonant with the share of channel profit that is influenced by the exogenously determined game structure—that is, consistent with the share of channel profit a player would obtain in the standard Stackelberg pricing model, in which the manufacturer and the retailer sequentially set prices to maximize respective profits. Therefore, when the manufacturer is the Stackelberg leader in a pricing game, the equitable payoff for the retailer would equal one-third of the total channel profit or one-half of the manufacturer's profit. The higher profit for the Stackelberg leader comes from its first-mover advantage relative to the follower under such a game structure, which grants the leader a higher profit than the follower. Thus, the newly proposed sequence-aligned ideal indicates that the equitable payoffs for the firms should be consistent with the exogenously determined game structure in the channel. To our best knowledge, this is the first research to empirically test how the exogenous channel structure versus the endogenous channel members’ decisions affect the formation of equitable payoffs for channel members.⁷

Note that the strict egalitarian ideal can be viewed as a special case of the sequence-aligned ideal. When both firms have the same moving advantages in the channel, such as in a simultaneous game, they deserve to have equal share of the total profit under the sequence-aligned ideal, a division of profits that coincides with the split under the strict egalitarian ideal. Thus, the use of a Stackelberg game is essential to separate the two fairness ideals, the strict egalitarian ideal and the sequence-aligned ideal.

Given our experimental design, each of all four fairness ideals can be represented by a unique value of τ.⁸ A value of τ = 1/2 corresponds to the strict egalitarian ideal. This is because the retailer's equitable payoff is equal to the manufacturer's profit from sales of product; that is, [τ/(1 - τ)]π_M = π_M, when τ = 1/2. A value of τ = 1/3 will successfully represent the sequence-aligned ideal in a standard Stackelberg pricing game because [τ/(1 - τ)]π_M = π_M/2 for τ = 1/3; that is, the retailer's equitable payoff is influenced by the exogenous game structure. In a similar fashion, we can show that the value of τ with the liberal egalitarian ideal is given by

\begin{matrix} τ & = {\begin{matrix} \frac{1}{2} & {if I}_{M} = I_{R} = 0 \\ \frac{I_{R}}{I_{M} + I_{R}} & otherwise \end{matrix} \end{matrix},

and the value of τ with the strict libertarian ideal is given by

\begin{matrix} τ & = {\begin{matrix} \frac{1}{2} & {if I}_{M} = I_{R} = 0 \\ \frac{I_{R} \times R_{R}}{I_{M} \times R_{M} + I_{R} \times R_{R}} & otherwise \end{matrix} \end{matrix} .

In Table 1, we summarize these four fairness ideals for ease of reference. Note that both the strict egalitarian ideal and the sequence-aligned ideal generate equitable payoffs that are independent of firms’ investments, while the retailer's equitable payoffs under both the liberal egalitarian ideal and the strict egalitarian ideal depend on firms’ payoffs that are affected by endogenous factors such as firms’ investments and contributions to the channel.

Table 1

FAIRNESS IDEALS

Fairness Ideals	τ
Sequence-aligned	1/3
Strict egalitarian	1/2
Liberal egalitarian	1=2, if I_M = I_R = 0; I_R=/(I_M + I_R), otherwise
Strict libertarian	1/2, if I_M = I_R = 0; I_R × R_R/(I_M × R_M + I_R × R_R), otherwise

Given the retailer's utility function and the manufacturer's profit function in the behavioral model with fairness, we can solve for the optimal wholesale and retail prices. Because both the analysis and results are lengthy, they appear in Web Appendix A.⁹

Different fairness ideals provide different predictions of firms’ pricing decisions, so we would expect that different τs would have different explanatory powers. If the best-fitting model among the four proposed models represents participants’ underlying fairness concerns, we would expect the τ of such model to be equal to the freely estimated τ in a full model. This leads to our second hypothesis:

H₂: The freely estimated ideal parameter τ is equal to the τ of the best-fitting model.

Channel Efficiency under Sequence-Aligned and Strict Egalitarianism Ideals

The current literature suggests that the principle of strict egalitarianism is the most prominent one to explain players’ concerns for fairness in distribution channels (Cappelen et al. 2007). With our introduction of the new fairness ideal of sequence-alignment, one interesting question arose: If a channel is guided under the new fairness ideal versus the prominent strict egalitarianism ideal, which ideal would lead to higher channel efficiency? Numerous research on distribution channels has argued that it is the concerns for fairness, rather than the structure of fairness, that helps build a harmonious and healthy relationship between channel members and helps improve the channel profit (Kumar 1996; Kumar, Scheer, and Steenkamp 1995). In Web Appendix A, we also echo this stream of research by showing that channel efficiency will improve under certain conditions of fairness concerns. Although we agree that concerns for fairness and trust between channel members can help generate greater channel profits than when firms are completely egocentric, we also would like to point out one important issue that has been neglected by the literature so far: fairness and channel structure, both of which may affect channel performance, might not be two independent forces in distribution channels. Rather, they can be intertwined with each other, and channel structure can strongly influence the perceptions of fairness. Such an influence may also affect the efficiency of a channel when firms have concerns of fairness.

Therefore, understanding what ideal applies to pricing decisions in channels is important not only for theory advancement but also from a practical perspective. Indeed, knowing the fairness ideal of the channel enables members to align their actions and has the potential to improve channel profits. This is because different ideals imply different optimal pricing strategies and different channel efficiency improvement regions. Knowing which ideal provides the larger channel improvement region is particularly important from a channel design standpoint, as it enables management to design a more efficient channel that increases general welfare. When focusing on this aspect, notably, we find that the sequence-aligned ideal improves the efficiency of the channel under a larger set of fairness conditions than the popular strict egalitarian ideal. Together with the fact that the strict egalitarian ideal is considered the most prominent and frequently referenced fairness ideal in the literature, this finding suggests that, contrary to lay beliefs, a channel generates more welfare when it recognizes the roles and the differences these roles imply for channel members than when it treats every member equally, as suggested by the social norm of strict equality. This important finding is summarized in the following result:

Result 1: The sequence-aligned ideal, τ = 1/3, leads to a higher channel efficiency improvement than the strict egalitarian ideal, τ = 1/2.

Web Appendix A provides proof for this result. The intuition for this result is that in recognizing the structure of the game, the sequence-aligned ideal does not impede channel members’ profit maximization. Indeed, the fairness disutility from unequal distribution of outcomes is minimized around the profit-maximization prices. In contrast, with the strict egalitarian ideal, the disutility for unequal outcome would be relatively large at the prices that maximize profit, which distorts the pricing strategies toward channel inefficiency.

QRE Model with Fairness Ideals

It is worth pointing out the necessity of considering bounded rationality in our behavioral model of fairness. Both bounded rationality and fairness concerns may influence players’ behaviors in a complex system such as a distribution channel. To discover whether fairness is an intrinsic preference by the players, we need to determine whether fairness concerns survive after controlling for bounded rationality. To solve this issue, we use a QRE model to capture the deviations from perfect rationality by channel members (Chen, Su, and Zhao 2012; Ho and Zhang 2008; Lim and Ho 2007; McKelvey and Palfrey 1995). Specifically, using a QRE model enables us to answer the following questions: (1) What is the driving force for deviations in players’ decisions? Are these deviations due to fairness concerns, bounded rationality, or both? (2) Can we differentiate and quantify fairness concerns and bounded rationality? (3) Are the manufacturer and retailer both equally boundedly rational in the game?

The key idea of the QRE framework is that decision makers will not always make the optimal decision, but they will make better decisions more often. This idea can be operationalized using a logit model. If we assume that decision makers make suboptimal choices that are subject to random errors that are i.i.d. as an extreme value distribution, then the probability of choosing any given option can be computed using a logit specification. More specifically, the probability for the retailer to choose a retail price at level p_j is given by

Prob (p = p_{j}) = \frac{e^{λ_{R} U_{R} (p_{j})}}{\sum_{k} e^{λ_{R} U_{R} (p_{k})}},

(4)

where the parameter λ_R refers to the retailer's degree of Nash rationality and increases as the retailer becomes more rational. It can be easily proved that when λ_R = 0, the probabilities for the retailer to choose each price level are the same, and the retailer is randomly choosing a price level. Intuitively, this happens because the weight attached to the utility carried by each choice is zero. Conversely, when λ_R = ∞, the retailer will choose the optimal price level with a probability of one. Indeed, in contrast to the case in which λ_R = 0, in this case the weight attached to the utility carried by each choice is infinity, so that the choice with the highest utility will always be chosen.

Thus, the QRE specification nests both perfect rationality and random choice in a flexible specification. Moreover, it has the advantage of requiring only minimal assumptions on the behavioral data. Indeed, although the QRE specification requires the econometrician to compute and compare the exact utility yielded by each alternative observed by a player, it assumes only that players choose a better alternative more often than a worse alternative.

The Experiment

Undergraduate students from two large public universities in the Midwest were recruited to act in the role of either the manufacturer or the retailer in each round. Each player was matched in each round with a different player playing the opposite role and played the first half of the rounds in the role of the manufacturer (retailer) and the second half in the role of the retailer (manufacturer). In the first stage of each round, the two players in the same channel simultaneously decided on the investments out of their initial endowment of E = 10 pesos. Because we are interested in understanding how players determine an equitable payoff, the return rates were varied across conditions so that the return rate for the investments could be either .2 or 1.2. The return rates were then crossed to create four treatment conditions (see Table 2) and participants were randomly assigned to one of these four conditions. The variation in return rates enables us to get the variance needed to estimate the model. We selected the values of the return rates so that the optimal investment decision for a profit-maximizing agent would always be to invest the entire endowment when facing a high return rate of 1.2 and never to invest anything when facing a low return rate of .2, irrespective of the return rate (and decision) of the other agent. This creates different incentives for participants to invest, which creates variation in investments and, thus, baseline demand. In addition, it enables us to differentiate between the effect of the contribution to the channel that is under the agents’ control (i.e., the investments) and the effect of the contribution that is outside the agent's control (i.e., the effective return to investments that is affected by return rates).

Table 2

PREDICTIONS OF THE STANDARD ECONOMIC MODEL

	Retailer
Manufacturer	R_R = 1.2	R_R = .2
R_M = 1.2
Investments	10.00, 10.00	10.00, 0
Prices	12.50, 18.75	7.50, 10.75
R_M = .2
Investments	0, 10.00	0, 0
Prices	7.50, 10.75	.50, .75

Notes: the first (second) number in each cell refers to the decision by the manufacturer (retailer).

In the second stage, players decided on prices. The player acting as the manufacturer decided on the wholesale price first. The player acting as the retailer was a follower and set the retail price after seeing the wholesale price. Therefore, in each round, each participant made two decisions, one on investment and the other on price. In the experiments, the available investment levels were 0, 2.5, 5, 7.5, and 10 pesos, and we have a = b = 1. Table 2 shows the theoretical predictions of both investments and prices.

A total of 150 undergraduate students took part in the experiments in exchange for cash payments that were contingent on their performance in the experiments. Two sessions were run for each of the four treatments. Each session consisted of approximately 20 participants, with the largest session having 20 participants playing 20 incentivized game rounds and the smallest session having 16 participants playing 16 incentivized rounds. Each session lasted for 75 minutes. Participants played two trial rounds against the computer to familiarize themselves with the game. Roles were randomly assigned at the beginning of the experiment and switched after half the rounds were played (e.g., a participant assigned to retailer in the first round would play as the retailer for the first half of the session and as manufacturer for the second half of the game). In each round, each participant was matched with a different participant playing the opposite role. Participants knew the assignment was randomized and changed at every round, and they did not know with whom they were paired. Such a setting is important so that the researcher can control for both the reputation effect and players’ long-term strategic considerations.

The experimental procedure was as follows. At the beginning of a session, participants were given a copy of the instructions, which were read aloud to them.¹⁰ The researcher then answered any questions participants raised. At the beginning of each round, each participant was informed of his or her role for that round. Then, players simultaneously decided how much of the endowment to invest in the channel. As we have discussed, players could choose to invest 0, 2.5, 5, 7.5, or 10 pesos out of their total endowment of 10 pesos. After investments were decided, players were informed about the amount of the investments, I_M and I_R, and the amount of baseline demand, BD = 1 + I_M × R_M + I_R × R_R.

In the pricing stage, the manufacturer in the channel acted as a Stackelberg leader. Thus, the manufacturer moved first to decide on a wholesale price, w, on the basis of investments and baseline demand. Manufacturers could decide among five wholesale prices: w₁ = BD/10, w₂ = BD/10, w₃ = BD/2, w₄ = 7BD, and w₅ = 9BD/10. The retailer moved second to decide on a retail price, p, on the basis of investments, baseline demand, and wholesale price. Similar to the manufacturer, the retailer could choose among five retail prices: p₁ = (BD - w)/10 + w, p₂ = 3(BD - w)/10 + w, p₃ = (BD - w)/10 + w, p₄ = 7(BD - w)/10 + w, and p₅ = 9(BD - w)/10 + w. The quantity sold was determined on the basis of the demand function D(p) = BD – p = 1 + I_M × R_M + I_R × R_R – p. For each unit sold, the manufacturer earned w pesos and the retailer earned p – w pesos. After the quantity sold was determined, both firms’ profits were calculated and communicated to both players. If any firm invested less than the initial endowment, the residual endowment was also added to the firm's final profit.

Participants were paid a show-up fee of $5 and a performance-based sum that was computed by adding up the payoffs from each experimental round and then converting them to U.S. dollars at a fixed rate. The total payment for each participant, including the show-up fee, ranged between $15 and $25. The average payment to participants was approximately $20. Participants were paid in cash at the end of each session. The experiments were conducted using z-Tree software (Fischbacher 2007).

Experimental Results

Given our experimental setup, it is easy to compute equilibrium investments and equilibrium prices for profit-maximizing agents. Table 3 and Figure 1 report the proportion of people choosing each investment level as predicted by the standard economic model and the actual investments observed in the experiments. The table indicates that participants’ decisions systematically deviate from the equilibrium predictions and that, depending on role and condition, approximately 40%–80% of participants did not choose the equilibrium investment level. Furthermore, we find that in the high return conditions, manufactures tend to invest more, and thus make fewer mistakes, than the retailers. In contrast, in the low return condition, because retailers invest less, retailers seem to make mistakes at a lower rate than the manufacturers. When looking at the trend of investments over time, we can see that in the low return condition, investments trend down toward zero, while in the high return conditions, investments do not increase over time. Thus, the low return condition pattern seems to suggest learning, whereas we find no evidence of learning in the high return condition. This makes it difficult to discern whether participants are truly learning.¹¹

Table 3

OPTIMAL AND ACTUAL INVESTMENT CHOICES

	Investment
	0	2.5	5	7.5	10
Manufacturer
R_M = .2
Optimal	100.00%	.00%	.00%	.00%	.00%
Actual	58.89%	22.01%	9.04%	7.73%	2.33%
R_M = 1.2
Optimal	.00%	.00%	.00%	.00%	100.00%
Actual	8.79%	8.65%	19.78%	24.45%	38.32%
Retailer
R_R = .2
Optimal	100.00%	.00%	.00%	.00%	.00%
Actual	61.66%	20.55%	9.97%	4.45%	3.37%
R_R = 1.2
Optimal	.00%	.00%	.00%	.00%	100.00%
Actual	20.73%	20.08%	23.36%	17.45%	18.37%

Figure 1

INVESTMENT CHOICES

Similarly, Table 4 and Figure 2 show the distribution of prices observed in the experiments given the actual investments. The standard model with perfect rationality and no fairness would predict all wholesale prices to be concentrated at w₃ and, given a wholesale w, the retail price to be concentrated at p₃. Again, we find that observed prices are different from the optimal prices, even after we take into account actual investments and, for retailer prices, manufacturer prices. Furthermore, we can see a systematic tendency to overprice. Only about 17% of manufacturers and 18% of retailers chose a price lower than the optimal price, while approximately 50% of both manufacturers and retailers chose a price higher than the optimal price. When observing the pricing trend over time, we see that there is no evidence of learning. Indeed, the share of people choosing each level of price fluctuates without any systematic increase or decrease, indicating that participants do not change their pricing behavior over the course of the game.

Table 4

DISTRIBUTION OF PRICE CHOICES

Wholesale Price	Retail Price
Wholesale Price	p₁	p₂	p₃	p₄	p₅	Total
w₁	.50%	.78%	.99%	.78%	1.70%	4.74%
w₂	1.13%	1.41%	3.89%	2.26%	3.39%	12.09%
w₃	1.77%	2.97%	13.22%	5.80%	7.28%	31.05%
w₄	1.13%	2.62%	6.29%	5.52%	6.44%	21.99%
w₅	4.31%	1.98%	6.93%	4.53%	12.38%	30.13%
Total	8.84%	9.76%	31.33%	18.88%	31.19%	100.00%

Figure 2

PRICE CHOICE

Estimation and Results

The experimental data show that both wholesale and retail prices are significantly different from the predictions of the standard economic model and that channel members are willing to punish each other even when such punishment is costly. Our behavioral model offers an explanation of these results by generalizing the standard economic model to incorporate fairness concerns that can significantly affect the interactions between channel members (Ho, Su, and Wu 2014; Kumar 1996; Kumar, Scheer, and Steenkamp 1995; Loch and Wu 2008) as well as bounded rationality (i.e., players are trying to maximize profits but make flawed decisions at the same time). To identify the bounded rationality in price decision making, we employ the QRE model (Ho and Zhang 2008; Lim and Ho 2007; McKelvey and Palfrey 1995). Note that given the structure of payoffs in our game, the QRE specification would predict participants’ decisions to be symmetrically distributed around the optimal prices in our game setting. In contrast, given the asymmetric impact of advantageous versus disadvantageous inequalities, fairness would predict participants’ decisions to be systematically skewed to the left or the right side of the optimal selfish price. This key feature enables us to identify and separately estimate the fairness and the QRE parameters.

In an effort to estimate fairness and QRE parameters using the data from the pricing stage, we develop a series of models. We can group the models into two categories: (1) the base model, in which both agents are boundedly rational and do not learn over time, and (2) the learning model, in which both agents are boundedly rational and learn over time. We summarize the notation used for the parameters in Table 5.

Table 5

NOTATION OF ESTIMATION RESULTS

Variable	Definition
λ_R	QRE parameter of the retailer
λ_M	QRE parameter of the manufacturer
α	Parameter of disadvantageous inequity
β	Parameter of advantageous inequity
τ	Parameter of fairness ideal

Base model

First, we estimated a base model using data from the pricing stage and assumed that the manufacturer and retailer are both boundedly rational. Note that when the manufacturer decides on the wholesale price w, (s)he does not know for sure what retail price, p, the boundedly rational retailer will choose. As a result, the manufacturer must make a decision in line with the expected profit (s)he would make from each possible wholesale price level. In contrast, when the retailer chooses the retail price, the wholesale price is already known. Thus, when setting wholesale prices, the manufacturer faces a more complicated decision than the retailer, who decides on the retail price p only after observing the wholesale price w. Under this framework, the log-likelihood for the estimation can be represented as follows:

LL = LLM + LLR, where

(5)

\begin{matrix} LLM & = \sum_{n} \sum_{i} y^{w = w_{i}} log [prob (w = w_{i})] \\ = \sum_{n} \sum_{i} y^{w = w_{i}} log (\frac{e^{λ_{M} {Eπ}_{M} (w_{i} {|p}_{j})}}{\sum_{k} e^{λ_{M} {Eπ}_{M} (w_{k} | p_{j})}}) \\ = \sum_{n} \sum_{i} y^{w = w_{i}} log [\frac{e^{λ_{M}}^{\sum_{j} prob (p = p_{j}) \times π_{M} (w_{i} {|p}_{j})}}{{\sum_{k} e^{λ_{M}}}^{\sum_{j} prob (p = p_{j}) \times π_{M} (w_{k} {|p}_{j})}}], and \end{matrix}

(6)

\begin{matrix} LLR & = \sum_{n} \sum_{i} y^{p = p_{j}} log [prob (p = p_{j})] \\ = \sum_{n} \sum_{i} y^{p = p_{j}} log [\frac{e^{λ_{R} U_{R} (p_{j})}}{\sum_{k} e^{λ_{R} U_{R} (Pk)}}] \cdot \end{matrix}

(7)

Here, U_R is the utility given by Equation 3, π_M = D(p) × w, and λ_M and λ_R are, respectively, the QRE parameters for the manufacturer and the retailer. Note that the probabilities of different retail prices affect the manufacturer's probabilities of choosing different wholesale prices. This requires us to simultaneously estimate the log-likelihoods for both manufacturer and retailer (i.e., LLM and LLR).¹²

We estimated different variants of this base model. First, we ran a model with no concerns for fairness and used it as a baseline to determine whether considering fairness concerns improves the explanatory power of the model. Next, we ran the four models corresponding to the four different fairness ideals. Finally, we ran a model in which we freely estimated the fairness ideal parameter τ.

Table 6 presents the estimation results. As the table shows, all the models that account for fairness have a significantly better fit than the baseline model, in which fairness is not considered. The estimated parameter of disadvantageous inequality α is significant across all fairness ideals. This result holds for both the baseline model without learning and the model with learning as well as for both the experiments with undergraduate participants and the experiments with MBA participants, as we discuss subsequently. Therefore, H_1a is supported. The estimated parameter of advantageous inequality β, however, is not significant with a one-shot game setting. Thus, the data do not support H_1b.¹³ When comparing the models that include the fairness ideals proposed by the literature with the sequence-aligned ideal, the Akaike information criterion (AIC) and Bayes information criterion (BIC) values suggest that the fairness ideal that best captures participants’ behaviors is the sequence-aligned ideal. Finally, when we freely estimate parameter τ, we find the estimated τ = .32 (p < .01) to be very close to the theoretical value of τ of the sequence-aligned ideal. Furthermore, we find that the model that estimates the fairness ideal freely does not fit the data better than the model that adopts the sequence-aligned ideal. This evidence indicates that the best-fitting model is the one that uses the sequence-aligned ideal, so we focus our discussion of the coefficients on the sequence-aligned model. In addition, because there is no significant difference between the freely estimated ideal parameter τ and the τ (= .33) of the sequence-aligned model (p = .74), H₂ is supported.

Table 6

ESTIMATION RESULTS OF THE BASE MODEL

	α = β = 0	Sequence-Aligned Ideal	Strict Egalitarianism	Liberal Egalitarianism	Strictly Libertarianism	Estimated Ideal
λ_Retailer	.14 (.01)^***	.08 (.01)^***	.13 (.01)^***	.13 (.01)^***	.14 (.01)^***	.09 (.01)^***
λ_Manufacturer	.01 (.00)^***	.02 (.00)^***	.02 (.00)^***	.02 (.00)^***	.02 (.00)^***	.02 (.00)^***
α	—	1.48 (.26)^***	.31 (.03)^***	.20 (.03)^***	.08 (.01)^***	1.57 (.40)^***
β	—	.00 (.14)	.00 (.21)	.00 (.13)	.00 (.13)	.00 (.00)
τ	—	—	—	—	—	.32 (.03)^***
N (Groups × Rounds)	1,414	1,414	1,414	1,414	1,414	1,414
Observations (N × Bins)	7,070	7,070	7,070	7,070	7,070	7,070
Log-likelihood	–4,466.2	–4,359.06	–4,377.23	–4,411.38	–4,440.08	–4,358.80
Likelihood ratio versus α = β = 0	—	214.28^***	177.94^***	109.64^***	52.24^***	214.8^***
AIC	8,936.4	8,726.12	8,762.46	8,830.76	8,888.16	8,727.6
BIC	8,950.13	8,753.57	8,789.91	8,858.21	8,915.61	8,761.92

***

p < .01.

Notes: Standard errors in parentheses.

Turning to the fairness coefficients of the sequence-aligned model, we find that there are significant concerns for distributive fairness in a channel in which both players are boundedly rational. The parameter of disadvantageous inequality α is equal to 1.48 and is significantly different from 0 (SE = .26, p < .01), while the parameter of advantageous inequality β is insignificant (β = .00, SE = .14). Because α is positive, the data suggest that an increase in inequality decreases the retailer's utility (see Equation 3) and that concerns exist regarding distributive fairness in the channel. In addition, because α > β, the estimation confirms that players are more dissatisfied with experiencing disadvantageous than advantageous inequity.

Finally, note that both players are boundedly rational. In particular, the QRE parameter for the retailer in the full model is given by λ_R = .08, while the QRE parameter for the manufacturer is λ_M = .02. Because a lower QRE parameter implies a higher rate of mistakes, the estimated results indicate that the manufacturer is more prone to mistakes when choosing prices than the retailer. Intuitively, the difference in the QRE parameters can be attributed to the manufacturer's facing more complicated decisions than the retailer. This is consistent with the experimental setup in which the manufacturer has to anticipate the retailer's boundedly rational responses when deciding on the wholesale price, whereas the retailer sets retail price p after observing the wholesale price w.

Learning model

In addition to the base model, we estimated a model in which participants are allowed to learn over time (Camerer and Ho 1999; Camerer, Ho, and Chong 2002, 2003; Chen, Su, and Zhao 2012).¹⁴ To represent learning, we allow the QRE parameter to change over time according to the following equation:

λ_{i} (t) = λ_{i} + (θ_{i} - λ_{i}) e^{- δ_{i} (t - 1)},

(8)

where i indicates whether the participant is a retailer or a manufacturer, and the bounded rationality parameter λ(t) decays exponentially over time. Note that λ_i(1) = θ_i and λ_i(∞) = λ_i. Therefore, θ_i can be interpreted as the initial rationality parameter and λ_i as the eventual rationality parameter, and δ_i captures the rate of learning. Given that the manufacturer and the retailer face different decision situations, we assume that the initial and the final rationality parameters differ for different types of players; we also assume that the manufacturer and retailer are learning at different rates.

As for the base model, we run a series of models that enable us to compare the standard model without fairness with the models that incorporate different fairness ideals. Again, we find that the model allowing for fairness dominates the standard model and that the fairness ideal that best represents the data is the sequence-aligned ideal (see Table 7). In addition, because each participant played multiple rounds of the game, the observations are likely to be correlated over rounds for each participant. To check whether the results hold after considering the possible correlation over rounds for each participant, we have computed the statistics with clustered standard errors when appropriate. The analysis using clustered standard errors does not change the results significantly.

Table 7

ESTIMATION RESULTS OF THE MODEL WITH LEARNING

	α = β = 0	Sequence-Aligned Ideal	Strict Egalitarianism	Liberal Egalitarianism	Strict Libertarianism
θ_Retailer	.11 (.02)^***	.06 (.01)^***	.09 (.01)^***	.11 (.02)^***	.09 (.02)^***
δ_Retailer	.01 (.05)	.00 (.02)	.00 (.01)	.01 (.01)	.01 (.01)
λ_Retailer	.83 (3.25)	1.49 (5.36)	2.00 (2.35)	.70 (.12)^***	1.72 (3.37)
θ_Manufacturer	.00 (.00)	.01 (.00)^***	.01 (.00)^***	.01 (.00)^***	.01 (.00)^***
δ_Manufacturer	.02 (.08)	.00 (.00)	.01 (.00)^***	.00 (.01)	.01 (.04)
λ_Manufacturer	.10 (.33)	2.00 (6.07)	.33 (.27)	.52 (1.11)	.04 (.03)^*
α	—	1.49 (.22)^***	.35 (.03)^***	.24 (.03)^***	.08 (.01)^***
β	—	.00 (.00)	.00 (.00)	.00 (.00)	.00 (.00)
N (Groups × Rounds)	1,414	1,414	1,414	1,414	1,414
Observations (N × Bins)	7,070	7,070	7,070	7,070	7,070
Log-likelihood	–4,460.5	–4,351.48	–4,368.82	–4,404.93	–4,431.99
Likelihood ratio versus α = β = 0	—	218.04^***	183.36^***	111.14^***	57.02^***
AIC	8,933	8,718.96	8,753.64	8,825.86	8,879.98
BIC	8,974.18	8,773.87	8,808.55	8,880.77	8,934.89

p < .1.

***

p < .01.

Notes: Standard errors in parentheses.

In the interest of space, we limit our discussion to the best-fitting model (i.e., the sequence-aligned model). In general, the results of the model with learning are comparable to the results of the base model without learning. Comparing across models suggests that the fairness parameters are similar, with disadvantageous inequality parameters significant in both the base and learning models (and not significantly different) and advantageous inequality parameters of both models not significant. The bounded rationality parameters are also consistent, suggesting that participants are boundedly rational and that the retailer tends to make fewer mistakes than the manufacturer. We speculate that the difference between the rationality parameters in the learning model is due to the higher complexity of the game faced by the manufacturer.

Even when considering learning, we find that the fairness parameters are remarkably consistent with the model without learning. Indeed, disadvantageous inequality is significant and close in magnitude to the estimates of the model without learning (α = 1.49, SE = .22, p < .01), while the advantageous inequality is again not significant (β = .00, SE = .00). Thus, the parameters confirm that the retailer has concerns for fairness and experiences disutility when its profit is less than half of the manufacturer's profit, but not when the profit is more than half of the manufacturer's profit.

Consistent with the patterns of pricing over time shown in Table 3, the learning parameters suggest that participants not only are boundedly rational but also are not learning over time. Indeed, the learning parameter δ is not significant for both manufacturer and retailer (δ_Retailer = .00, SE = .02; δ_Manufacturer = .00, SE = .00), suggesting that there is no significant learning over time. This inability to learn might be due to the experimental protocol, which randomly matches participants at each round and effectively makes each round a one-shot game. We also find that the initial QRE parameter θ is lower than the QRE parameter estimated in the base model for the retailer, while the final QRE parameter λ is higher (though not significant) than the QRE parameter estimated in the base model. This might indicate that participants are learning over the course of the game, but that the number of rounds in our experiment is not sufficient to achieve a significant improvement in their performance.

Discussion

The estimated models provide converging evidence that channel members, and retailers in particular, display fairness concerns. Perhaps unsurprisingly, participants seem to display a higher concern for disadvantageous inequality than for advantageous inequality. One reason why advantageous inequality might not look like a significant concern for participants is that the concern for profits might overshadow the concern for advantageous inequality to a degree that makes it difficult for the econometrician to identify the latter. Moreover, the manufacturers’ beliefs about retailers’ preference play a role in the estimated parameters; thus, the insignificant result might be due in part to manufacturers believing that retailers do not care about advantageous inequality.

We also find that the best-fitting model is the sequence-aligned model, suggesting that exogenous factors such as the characteristics of the channel play a more important role than endogenous factors such as the investments made by participants. In addition, the fit of the sequence-aligned model versus the strict egalitarian model suggests that participants are not trying to minimize unequal splits of profits. Instead, they seem to be willing to tolerate unequal splits of profits, as long as the differences in profits are warranted by differences in the roles of the channel members and as long as the other channel member does not take advantage of his or her privileged position.

Robustness Check

We collected the data from the undergraduate participant pool. One might wonder whether our results are due to participants’ inexperience with the decision at hand. Such a concern seems to be particularly relevant as the number of participants who make suboptimal decisions is very high for both investments and pricing. Although previous research has suggested that there is no significant difference between using experienced managers and students (Bolton, Ockenfels, and Thonemann 2012; Croson 2007), to check the robustness of our results, we collected an additional sample of participants who are experienced with managerial decisions. We recruited 24 MBA students from a large midwestern university and ran two additional sessions of the experimental game. The MBA experiment followed the same experimental procedure as the one for undergraduate students, and payments followed the same structure. We found that the MBA participants made fewer mistakes than the undergraduate students but showed similar concerns for fairness.

Indeed, the distribution of investments (reported in Table 8 and Figure 3) highlights that the MBA participants deviated less from the optimal investment level than the undergraduate sample. With the exception of retailers facing a high return rate, the majority of MBA participants (56%–67%) chose the optimal investment. Similar to the undergraduate sample, the MBA participants’ investments seem to converge to zero in the low return condition, whereas they do not increase to converge to ten for the high return condition. For pricing choices (reported in Table 9 and Figure 4), we observe that, similarly to the undergraduate participants, approximately 30% of both manufacturers and retailers chose the optimal price. However, for MBA participants, the tendency to overprice is exacerbated in retailers, with approximately 60% of MBA participants overpricing versus about 50% of undergraduate participants doing the same. This tendency seems to be exacerbated over time, but only for retailers. Like the undergraduate sample, MBAs do not systematically move their pricing choices to the optimal choice.

Table 8

OPTIMAL AND ACTUAL INVESTMENT CHOICES (MBA SAMPLE)

	Investment
	0	2.5	5	7.5	10
Manufacturer
R_M = .2
Optimal	100.00%	.00%	.00%	.00%	.00%
Actual	55.56%	19.44%	19.44%	2.78%	2.78%
R_M = 1.2
Optimal	.00%	.00%	.00%	.00%	100.00%
Actual	5.56%	9.72%	9.72%	8.33%	66.67%
Retailer
R_R = .2
Optimal	100.00%	.00%	.00%	.00%	.00%
Actual	55.56%	23.61%	16.67%	2.78%	1.39%
R_R = 1.2
Optimal	.00%	.00%	.00%	.00%	100.00%
Actual	41.67%	9.72%	16.67%	8.33%	23.61%

Figure 3

OPTIMAL AND ACTUAL INVESTMENT CHOICES (MBA SAMPLE)

Table 9

DISTRIBUTION OF PRICES (MBA SAMPLE)

	Retail Price
Wholesale Price	p₁	p₂	p₃	p₄	p₅	Total
w₁	.00%	.69%	2.08%	.00%	4.17%	6.94%
w₂	.00%	.69%	4.86%	.00%	2.78%	8.33%
w₃	1.39%	1.39%	13.19%	11.81%	4.17%	31.94%
w₄	.69%	1.39%	6.94%	4.86%	6.94%	20.83%
w₅	2.08%	.69%	4.17%	1.39%	23.61%	31.94%
Total	4.17%	4.86%	31.25%	18.06%	41.67%	100.00%

Figure 4

DISTRIBUTION OF PRICES (MBA SAMPLE)

When we estimate our base model on the MBA participants’ data (Table 10), we find that the sequence-aligned ideal still fits the data the best among all four ideals. Moreover, when we freely estimate parameter τ, we find the estimated τ = .33 (SE = .74, n.s.). Although the estimated τ is not significant, it is very close to the theoretical value of τ of the sequence-aligned ideal. Turning to the coefficient in the sequence-aligned model, we find a similar concern for fairness in the MBA population as in the undergraduate population. Indeed, MBA participants are also concerned about advantageous inequality (α = 1.95, SE = .82, p < .01), while the parameter of advantageous inequality β is insignificant (β = .00, SE = .32). In contrast, we find a much higher rationality parameter for MBA participants than undergraduate participants for both retailers (t = 2.28, p < .05) and manufacturers (t = 7.86, p < .01). By examining the learning model (Table 11), we find that, compared with the undergraduate sample, both MBA retailers and manufacturers display a higher degree of rationality from the beginning (retailers: t = 3.96, p < .01; manufacturer: t = 6.29, p < .01), but, like the undergraduate sample, they do not learn over time. Indeed, although the final rationality coefficient λ is significant, the learning rate δ is not significant, and the estimated λ is not statistically different from the estimated θ (retailers: t = 1.12, p = .26; manufacturers: t = 1.39, p = .17).

Table 10

ESTIMATION RESULTS OF THE BASE MODEL (MBA SAMPLE)

	α = β = 0	Sequence-Aligned Ideal	Strict Egalitarianism	Liberal Egalitarianism	Strictly Libertarianism	Estimated Ideal
λ_Retailer	.28 (.05)^***	.16 (.05)^***	.21 (.05)^***	.28 (.05)^***	.30 (.06)^***	.15 (.26)
λ_Manufacturer	.06 (.01)^***	.07 (.02)^***	.07 (.02)^***	.05 (.01)^***	.05 (.01)^***	.08 (.08)
α	—	1.95 (.82)^***	.48 (.13)^***	.22 (.08)^***	.03 (.01)^***	1.83 (10.33)
β	—	.00 (.32)	.00 (.41)	.00 (.21)	.00 (.21)	.00 (.00)
τ	—	—	—	—	—	.33 (.74)
N (Groups × Rounds)	144	144	144	144	144	144
Observations (N × Bins)	720	720	720	720	720	720
Log-likelihood	–446.27	–422.92	–423.36	–440.26	–443.32	–422.67
Likelihood ratio versus α = β = 0	—	46.7^***	45.82^***	12.02^***	5.9^**	47.2^***
AIC	896.54	853.84	854.72	888.52	894.64	855.34
BIC	905.07	872.16	873.04	906.84	912.96	878.24

p < .05.

***

p < .01.

Notes: Standard errors in parentheses.

Table 11

ESTIMATION RESULTS OF THE MODEL WITH LEARNING (MBA SAMPLE)

	α = β = 0	Sequence-Aligned Ideal	Strict Egalitarianism	Liberal Egalitarianism	Strict Libertarianism
θ_Retailer	.31 (.13)^**	.22 (.08)^***	.28 (.10)^***	.35 (.13)^***	.35 (.16)^**
δ_Retailer	1.52 (3.67)	1.05 (.90)	.70 (.91)	.93 (1.40)	1.36 (3.20)
λ_Retailer	.26 (.05)^***	.12 (.04)^***	.18 (.06)^***	.25 (.06)^***	.28 (.06)^***
θ_Manufacturer	.03 (.02)	.05 (.02)^**	.05 (.03)^*	.02 (.02)	.02 (.02)
δ_Manufacturer	.49 (.83)	.54 (.69)	.56 (.99)	.42 (.76)	.34 (.59)
λ_Manufacturer	.06 (.03)^**	.10 (.03)^***	.09 (.03)^***	.08 (.04)^*	.08 (.05)
α	—	1.95 (.68)^***	.48 (.11)^***	.23 (.07)^***	.03 (.01)^**
β	—	.00 (.00)	.00 (.00)	.00 (.00)	.00 (.00)
N (Groups × Rounds)	144	144	144	144	144
Observations (N × Bins)	720	720	720	720	720
Log-likelihood	–445.68	–421.14	–422.50	–439.06	–442.06
Likelihood ratio versus α = β = 0	—	49.08^***	46.36^***	13.24^***	7.24^**
AIC	903.36	858.28	861	894.12	900.12
BIC	930.836	894.914	897.634	930.754	936.754

p < .1.

p < .05.

***

p < .01.

Notes: Standard errors in parentheses.

These results provide strong support for the robustness of our estimates of the concerns for fairness and the factors that affect them. One might worry that only unsophisticated participants unused to making managerial decisions could be driven by fairness. However, when we compare the unexperienced undergraduate population with the more experienced MBA population, we find a significant difference in the degree of rationality between the two populations, but such difference in rationality does not affect any of the results on fairness. In both populations we find that (1) participants care for fairness; (2) participants are more concerned about disadvantageous inequality than advantageous inequality; and (3) exogenous factors, such as the structure of the game, matter more in determining the fair outcome of the game than endogenous factors, such as investment and contribution.¹⁵

Discussion and Conclusion

In this article, we propose a behavioral model that incorporates both concerns for fairness and bounded rationality in a dyadic channel, in which the manufacturer acts as a Stackelberg leader in setting prices and the retailer acts as a follower, to examine how fairness concerns and bounded rationality may influence firms’ decisions in a channel. In addition, through such an enriched model, we investigate how equitable payoffs are determined in the fair channel and propose a new principle of fairness (i.e., the sequence-aligned fairness ideal) that has never been investigated in the literature. We also experimentally investigate the theoretical predictions on prices using laboratory data. Our research makes the following contributions to the literature.

First, to the best of our knowledge, our research is one of the first to empirically study fairness ideals in a complex system such as a distribution channel. We provide an estimation of fairness parameters in such a context. The estimation results suggest that there are significant fairness concerns in channels in which decision makers’ behaviors are affected by many factors such as multiple decisions, response uncertainty and bounded rationality, and an indirect link between firms’ investments and payoffs. By studying such a complicated model, we are able to investigate whether fairness concerns are managerially relevant in the channel context and how they compare with profit-maximization motives. We find that fairness not only is present in channel but also can be quite strong compared with profit motives. This research finding provides evidence that fairness can significantly affect firms’ decisions in channels and thereby offers support to the notion that fairness can modify channel relations.

Second, our research contributes to the understanding of the determinants of equitable payoffs between fair-minded agents in business relations. We compare three commonly proposed fairness principles (i.e., strict egalitarianism, liberal egalitarianism, and strict libertarianism; Cappelen et al. 2007) with a newly proposed principle of fairness studied for the first time in literature—the sequence-aligned ideal—which reflects the influence of exogenous game structure on perceptions of fairness. The comparison between the principles suggests that the sequence-aligned ideal significantly outperforms other ideals in describing participants’ behaviors in our experiments. The newly established ideal is particularly interesting and important because it reflects the concept that the equitable payoff for the retailer is consistent with the ratio of players’ profits in the standard Stackelberg game and suggests that exogenous game structure does affect what is perceived as “fair.” This finding indicates that it is fair for the Stackelberg leader (i.e., the manufacturer) to obtain a higher payoff than the follower (i.e., the retailer). In addition, our results also suggest that, contrary to lay beliefs, the channel under the sequence-aligned ideal outperforms the channel under the most prominent and frequently referenced strict egalitarianism ideal in channel efficiency. So the channel with equity under the sequence-aligned principle can lead to a higher efficiency than the channel with equality under the principle of strict egalitarianism. These findings contribute to the literature by showing how game structure influences channel members’ beliefs of deserved profits and how such beliefs affect firms’ decisions and eventually guide the realization of profits for all the members in a channel.

Finally, our study includes inclinations for both social preferences and bounded rationality, and we differentiate and quantify these effects through incentive aligned experimental studies. On the one hand, we find that both manufacturers and retailers make errors in their decisions, albeit to different extents. Because the manufacturer is the first mover in a Stackelberg game and sets its wholesale price before the retailer decides on the retail price, the manufacturer faces a more complex task than the retailer. This is confirmed by our estimation: the QRE parameter for the manufacturer is significantly smaller than that for the retailer, indicating that the manufacturer is less rational than the retailer. On the other hand, we also find that even after accounting for such bounded rationality, fairness concerns still significantly affect firms’ decisions. This implies that deviations in players’ pricing decisions from predictions of the standard economic model are not entirely due to errors in their decision making—concerns for fairness indeed can be an important factor influencing the interactions between firms in distribution channels.

As such, our results emphasize the need to account for fairness in modeling firm behavior. This need is not diminished in complex contexts, such as in a channel, or when participants are more sophisticated, as evidenced by the comparison between the MBA and undergraduate populations. In other words, it is not the sophistication or the lack thereof that leads participants to a semblance of fairness; rather, a genuine concern makes people fair-minded. Furthermore, we are able to characterize the type of factors that can affect fairness concerns. We find that endogenous participants’ decisions (i.e., how much they invest in the channel) play a secondary role in determining fairness. In contrast, the factors that are best able to explain what determines the fair outcome are exogenous factors. In our experiment, the exogenously determined structure of the game is what determines the fair outcome. Researchers and practitioners alike can use this knowledge regarding the factors that are likely to affect fairness to model and forecast the effect of fairness. Thus, our research provides some findings that are rather notable and important for both academics and practitioners in terms of how to understand the effect of fairness concerns in a distribution channel and how to better manage fairness concerns to improve channel relationships and efficiency.

Footnotes

1

A short list of research on this topic includes Anderson and Simester (2004, 2008, 2010), Camerer (2003), Charness and Rabin (2002), Fehr, Klein, and Schmidt (2007), Fehr and Schmidt (1999), Goldfarb et al. (2012), Güth, Schmittberger, and Schwarze (1982), Hackett (1994), Ho and Su (2009), Kahneman, Knetsch, and Thaler (1986a, b), Macneil (1980), Olmstead and Rhode (1985), and .

2

The research includes Anderson and Weitz (1992), Caliskan-Demirag, Chen, and Li (2010), Corsten and Kumar (2003, 2005), Frazier (1983), Hackett (1994), Katok and Pavlov (2013), Katok and Wu (2009), Kaufmann and Stern (1988), Kumar (1996), Kumar, Scheer, and Steenkamp (1995), Loch and Wu (2008), Macneil (1980), McCarthy (1985), Meyer et al. (2010), Olmstead and Rhode (1985), and Scheer, Kumar, and Steenkamp (2003).

3

We thank an anonymous reviewer and the associate editor for this suggestion.

4

Web Appendix A provides the solutions for the standard economic model with continuous prices and investments. The results with discrete prices and investments are tedious, with similar insights, and are therefore omitted. The analysis is available from authors on request.

5

We also estimated a model in which the manufacturer was allowed to display concerns for fairness and found that both advantageous and disadvantageous inequality coefficients were insignificant. We speculate this might be due to concerns for profit maximization overshadowing the concerns for fairness when the decision faced by the participant is highly complex.

6

We assume the retailer compares profit from sales of product π_R with equitable payoff [τ/(1 - τ)]π_M, which is a function of the manufacturer's profit from sales of products as well. The reason for such a specification is that firms’ pricing decisions in the pricing stage will affect only their profits from sales of product, given their investment amounts. The residual of endowment, E – I_j (j = M, R), in contrast, is independent of firms’ pricing decisions.

7

We thank the associate editor for suggesting that we emphasize the influence of game structure on fairness perceptions.

8

Because α and β measure the degree of fairness concerns for a decision maker but not his or her belief about what kind of deal is fair, they are independent of the fairness ideal. Therefore, we cannot use parameters α and β to test different fairness ideals. We thank the associate editor for suggesting that we consider this issue.

9

Because the retailer's utility and the manufacturer's profit are complicated nonlinear functions of investments in the behavioral model with fairness, there is no closed-form solution for investments. In addition, both the retailer's utility and the manufacturer's profit are highly nonlinear functions of prices and investments in the behavioral model with bounded rationality owing to unique QRE model specifications. Thus, we follow the literature to solve prices and investments numerically.

10

For the instructions used in Experiment 2 with R_M = .2 and R_R = .2, see Web Appendix B. The instructions for other conditions are available from the authors on request.

11

We assume that participants have no cross-role learning by observing their partner playing. We thank the Editor in Chief for pointing out this limitation.

12

We estimated the maximum likelihood using the fmincon routine in Matlab. The manufacturer and retailer log-likelihoods were jointly maximized. Parameters were restricted to respect the assumptions of the theory (α ≥ β ≥ 0, λ_R ≥ 0, and λ_M ≥ 0).

13

We also conducted experiments with fixed-matching protocol in which participants play a repeated game with fixed partners. The data estimation suggests that both α and β are significant with fixed-matching protocol. The results are available from the authors on request.

14

We thank the associate editor and reviewers for suggesting to incorporate this analysis.

15

In addition to the reported robustness check, we also ran several modified versions of the experiment on an undergraduate population with a total of an additional 332 participants across different experimental treatments. We obtained very similar results to the reported experiment: (1) participants cared about fairness, (2) participants cared more about disadvantageous inequality than advantageous inequity, (3) the best-fitting model was the sequence-aligned model, and (4) retailers displayed higher rationality coefficients than manufacturers. These modified experiments included the following modifications: (1) continuous investment and prices, (2) discrete investment and continuous prices, (3) three levels of discrete investment and prices, and (4) repeated matching protocol with discrete investments and continuous prices. The results of these estimates are available from the authors.

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