The Incentive Effects of Tournaments and Peer Effects in Team Production: Evidence from Esports

Abstract

This paper examines the incentive effects of increased prize differentials and productivity spillovers from substitute coworkers within the context of esports. A direct behavioral measure called “actions per minute (APM)” is utilized to gauge Dota 2 players’ on-field exertion of effort dedicated to winning the game. The results based on empirical analysis support the incentive effects of the convex prize structure of esports tournaments on eliciting effort. Further investigation indicates that the incentive effects of high-stakes esports tournaments are more a result of the size of total prize than the relative prize distribution. It is also found that players who serve subordinate roles are more likely to engage in shirking behavior in the presence of teammates with similar roles.

Keywords

esports tournament theory peer effects team production double-elimination tournament

Introduction

Tournament theory describes a compensation arrangement wherein wages are not based on workers’ marginal products but completely determined by their relative outputs or rank orders in a tournament-style contest (Lazear & Rosen, 1981). Since its inception, tournament theory has been often used to rationalize the disproportionately high payments to employees who stand out from the competition, such as chief executive officers, tenured professors, and top salespeople (Connelly et al., 2014; Ehrenberg & Bognanno, 1990b). Many labor economics studies found that large managerial pay gaps provided effective incentives to improve enterprise performance (Elsayed & Elbardan, 2018; Eriksson, 1999; Heyman, 2005; Lin et al., 2013). Meanwhile, there has been a growing body of empirical research, spearheaded by Ehrenberg and Bognanno (1990a, 1990b), that examined tournament theory using data from professional sports. It is worth noting that most of the studies in this area focused on golf (Ehrenberg & Bognanno, 1990a, 1990b; Orszag, 1994) and racing sports (Becker & Huselid, 1992; Humphreys & Frick, 2019; Lynch & Zax, 2000; Maloney & McCormick, 2000) by utilizing performance metrics like total score, finishing time/position, and average speed to infer athletes’ on-field effort exertion. Similarly, Gilsdorf and Sukhatme (2008) capitalized on a tennis dataset to test Rosen (1986) multistage tournament model, in which promotions and eliminations occur sequentially. In particular, they confirmed the effectiveness of the convex prize structure, with rewards being highly skewed towards the top ranks, in increasing the stronger player's probability of winning (i.e., selecting the best contestant). However, their remarks were primarily based on conjectures regarding tennis players’ effort choices under certain assumptions rather than a direct probe into the issue. In the sports economics literature, therefore, empirical research aimed at examining the incentive effects of tournament prize structures remains restricted to performance or outcome-based inferences about effort.

Behavioral data from electronic sports (also known as esports), where human-to-human gaming contests are facilitated by electronic devices (Hamari & Sjöblom, 2017) and Internet technologies (Wagner, 2006), can help expand the scope of empirical research on tournament theory (Coates & Parshakov, 2016; Shenkman et al., 2022). Over the past decade, the rise of esports has precipitated the evolution of video gaming from a conventional leisure activity to a professional sport (Hamari & Sjöblom, 2017; Seo & Jung, 2016). The competitive nature of esports (Mao, 2021) is sufficiently embodied by its “play to win” spirit (Cullen, 2018) as well as its contexts, such as physical sports, fighting contests, and military battles (Burk, 2013). Accordingly, esports and traditional sports are comparable in many aspects (Ward & Harmon, 2019). For example, the survey results of Hamari and Sjöblom's (2017) study, based on the motivation scale for sports consumption, indicated that people watched esports to escape from daily routines, acquire game-related knowledge, and enjoy novel and thrilling elements. In addition to fan interest, the similarities between esports and traditional sports can be seen from the ever-increasing number of formally organized esports tournaments with considerable monetary rewards and a growing cohort of professional esports players who are able to live entirely off prize money (Seo & Jung, 2016). According to Esports Earnings (https://www.esportsearnings.com), a community-driven website that compiles esports-related earnings from public sources, there has been 127 esports tournaments with a prize pool of at least US$1 million and 483 esports players whose career earnings exceed US$300,000 as of May 2021. With increased emphasis on the participants’ skills and competencies, esports is already beyond a gaming activity merely for amusement purpose.

In the realm of esports, actions per minute (APM), which is calculated by dividing the number of actions with the number of minutes where the actions spread in time, can serve as a direct behavioral measure of the effort put forth by individual competitors. Technically as a record of mouse and keyboard inputs, APM gauges the frequency with which an esports player performs in-game actions such as selecting units and issuing orders. While it is often considered as an indicator of gaming proficiency (Lewis et al., 2011; Thompson et al., 2013), APM is also an ideal proxy for esports players’ exertion of effort because the only means they can strengthen their influence on the game is increasing user input frequency provided that “the primary aspects of the sport are facilitated by electronic systems” (Hamari & Sjöblom, 2017, p. 213). For example, Figure 1 illustrates that esports success, represented by players’ career win rates, is positively correlated with their career median APMs, which holds true among both professional and amateur players. With this in mind, the present paper leverages a novel dataset of player APMs and tournament prizes from Dota 2, one of the most popular esports game titles, to empirically examine the incentive effects of the convex payoff structure (see Figure 2) on contestants’ effort choices (Lazear & Rosen, 1981; Rosen, 1986), with the related hypothesis being proposed as follows:

Hypothesis 1. Prizes that increasingly concentrate in the top ranks elicit greater effort from players.

Additionally, considering that Dota 2 competitions involve a high degree of teamwork, which is not uncommon in the field of esports (Shenkman et al., 2022), this paper analyzes the interactions between team members through the lens of productivity spillovers. In labor economics, substantial attention has been devoted to the discussion of peer effects on effort exerted by coworkers in a team production process (Alchian & Demsetz, 1972; Arcidiacono et al., 2016; Cornelissen et al., 2017; Herbst & Mas, 2015; Ichino & Maggi, 2000; Mas & Moretti, 2009; Winter, 2004). Some researchers in this field are particularly interested in investigating the relationship between the complementarity and substitutability of coworkers and team productivity (Büyükboyacı & Robbett, 2017; Goerg et al., 2010; Gould & Winter, 2009). To be more specific, it is posited that whereas workers with complementary skills should generate positive productivity spillovers, workers who are substitutes tend to be free riders undermining team productivity. Within the game of Dota 2, each hero (or avatar) can fulfill a certain set of tactical roles, such as Carry, Nuker, and Initiator, that implement strategies and contribute to final victory. While there clearly are complementary roles (e.g., Carry and Support) in the game, this paper does not expand on the topic of complementarity since it would incur a lengthy clarification regarding the gameplay of Dota 2. Instead, we mainly focus on players’ shirking behavior, as measured by reduced APMs, in the presence of teammates with similar tactical roles (i.e., the substitutability of coworkers). Accordingly, we formulate the following hypothesis:

Hypothesis 2. Players reduce their exertion of effort in the presence of teammates with similar tactical roles.

The analysis of esports data using a random effects model produces evidence indicating that a US$1 million increase in prize differential improved roughly 2% exertion of effort, which is consistent with Rosen (1986) predictions as well as labor economists’ empirical findings (Elsayed & Elbardan, 2018; Eriksson, 1999; Heyman, 2005; Lin et al., 2013). However, a further investigation differentiating the magnitude and distribution of prizes suggests that the incentive effects were primarily accounted for by the former variable. That is, players’ increased effort should be attributed more to the inter-tournament effect, the difference in the overall size of prize pool between tournaments, than the intra-tournament effect, the relative distribution of prizes within a single tournament. In addition, the analysis reveals that only players serving subordinate roles exhibited a clear-cut tendency to reduce effort when teammates with similar roles were present.

Backgrounds

Dota 2 is a popular esports game that falls into the genre of multiplayer online battle arena, which is seen as a hybrid of real-time strategy, role-playing, and action games. Its gameplay occurs when two teams consisting of five players, each in control of a drafted hero with different abilities, accumulate experience points and gold that increase combat statistics and battle on a specified map. The ultimate goal for winning the game is to destroy the opposing team's main structure named “the Ancient” located deep in the base. According to the game community (https://liquipedia.net/dota2/Hero_Roles), there are nine distinctive types of roles in Dota 2 that heroes can play to implement the team's strategic and tactical plan, including Carry, Nuker, Initiator, Disabler, Durable, Escape, Support, Pusher, and Jungler. For example, whereas Support roles are mainly responsible for protecting, buffing (i.e., providing beneficial effects), and healing their teammates, Carry roles are expected to deal the largest amount of damage and lead (or “carry”) the team to victory. A hero can belong to multiple roles at the same time and a more diverse composition of roles can help build a well-rounded team that has greater tactical flexibility. Furthermore, competitive Dota 2 play typically adopts the so-called Captains Mode (https://liquipedia.net/dota2/Game_Modes) for drafting heroes, in which two team captains are responsible for banning unwanted heroes and picking wanted heroes in turn from a random pool. After this ban-and-pick procedure, each team's players can select a hero from those chosen by their captain.

Dota 2 tournaments are renowned for their high prizes, with The International (TI) 2019 being touted as the single event in esports history that has the largest prize pool of over US$34 million (https://dota2.prizetrac.kr/international2019). Premium Dota 2 tournaments, whose total purse are no less than US$1 million, are typically carried out in a double-elimination format (http://www.dota2.com/international/standings). First, 16 or 18 teams are divided into two round-robin groups and play several best-of-n (BO $n$ ) series in the group stage, and the surviving 16 teams advance to the main event. Then, the top four finishing teams from both groups are assigned to the upper bracket (UB) and the bottom four to the lower bracket (LB). The first round of the LB is implemented as single elimination using BO1. Every other round of both brackets is played in a BO3 series, with the exception being the Grand Finals, which is played between the winners of the UB and LB in a BO5 series. Notably, the double-elimination tournament format downgrades any losers from the UB to the LB instead of excluding them immediately, which grants them an extra chance to pursue the trophy and grand prize.

Two player and gameplay-related factors are believed to affect Dota 2 players’ APMs. To illustrate, Figure 3 shows the minute-by-minute frequencies of in-game actions performed by ten players in a Dota 2 match. There are two discernible patterns. First, the numbers of actions generally begin at a relatively high level, which is a result of players’ habitual behavior termed as APM “spamming” (i.e., artificially increasing APM). Esports players usually do so for the purposes of warming up and impressing audience, albeit without any material gain especially at the starting stage of the game. Second, the numbers of actions sometimes drop to a fairly low level that is even close to zero because the hero in question is being killed and remains inactive until it respawns, during which period the player temporarily loses the control over the hero.¹

Model

To test Hypothesis 1 by establishing the relationship between prize differentials and effort intensity in Dota 2 tournaments, we formulate the following regression model:

E_{i h j r t} = β_{0} + P_{i} + H_{h} + β_{1} D T R_{i j r t} + β_{2} P D_{r t} + β_{3} U B_{r} + β_{4} P D_{r t} * U B_{r} + β_{5} W P D_{i r t} + γ^{'} R_{r} + θ^{'} {S u b}_{i j r t} + ε_{i j r t}

(1)

In Equation 1, E_ihjrt is player i's exertion of effort controlling hero h, proxied by his APM statistic, in match j of round r in tournament t. P_i is the player-idiosyncratic random effect introduced to address personal factors such as talent and the APM spamming preference associated with player i. Whereas the mechanism of APM spamming has been explained in the previous section, there is a need to elucidate the relationship between talent and APM. In addition to talent in gaming proficiency, APM can be used to measure an esports player's situational effort exertion. An analogy to APM within the context of sports is marathon runners’ finishing times. While talented runners are closely ranked with exceptional finishing times, they could still improve their performance to some extent by putting forth extra effort if they have a strong willingness to do so (Allen et al., 2017). H_h is the hero-specific random effect intended to capture the mechanical complexity of hero h, which depends on the hero's abilities, tactical roles, and play styles. Pertinent to the gameplay of Dota 2, DTR_ijrt is an important control variable that impacts how large the APM value would be realized. As its name suggests, APM is calculated by dividing the total number of a user's mouse and keyboard inputs by the number of minutes in a match. On the one hand, the more often a hero is trapped in the status of being dead (or inactive), during which time the player is unable to effectively control the hero and has to wait until it respawns, the smaller the total number of in-game actions would be. On the other hand, the duration of the match also plays a non-trivial role since a longer game time can entail more occurrences of kills and deaths. With this in mind, we construct a ratio of dead time relative to the duration of the match to control for the mitigating effect of the hero' deaths on the controlling player's APM statistic.

The variable of main interest PD_rt is the prize differential measured as the difference between tournament t's top prize and the amount awarded to the losers in round r. According to Gilsdorf and Sukhatme (2008), this differential should be positively correlated with the inter-rank spreads if the prize distribution is convex in rank order. In Dota 2, it is a common practice for the winning team to evenly split the prize money, after subtracting the cuts for the organization and the coach if required, among the five main players (https://www.esportsearnings.com), though each team may have its own allocation formula. Although Dota 2 players control in-game heroes assigned with different tactical roles, which are not directly substitutable within the team, their individual effort decision-making should positively respond to the increased prize differential. Research has found that, when a bonus is awarded in proportion to the output of the whole team, members tend to positively adjust their effort exertion as relative rewards escalate (Danilov et al., 2019). In theoretical analysis, economists also assume the prize to be shared equally between team members, even if their efforts are not perfectly substitutable (Fu et al., 2015; Shenkman et al., 2022).

UB_r is a dummy variable that equals 1 if round r occurs in the UB and otherwise 0. Specifically, it is used to address the double-elimination tournament format as well as detect the behavioral difference in effort supply between observations competing in the UB and LB, where they might behave inconsistently because of a second chance granted to the UB teams (Huang, 2016). Furthermore, an interaction term PD_rt*UB_r is introduced to test for whether players’ effort decision-making responds to prize differential differently contingent on being in the UB or LB. Accordingly, β₂ only measures the impact of prize differential on players’ effort exertion when UB_r equals zero (i.e., in the LB). For evaluating that impact in the case of UB, we need to add β₄ to β₂.

The relevant literature also suggests that overlarge skill differences can cause adverse incentive effects on players’ exertion of effort (Brown, 2011). That is, when the talents of competitors are grossly unbalanced, the optimal option for the less talented player(s) could be to reduce effort and even give up. To control for the potential adverse incentive effects, this paper first converts pregame betting odds in round r into implied wining probabilities using the equations as follows:

I m p l i e d P r o b a b i l i t y = {\begin{matrix} \begin{matrix} \frac{| o d d s |}{(| o d d s | + 100)} * 100 %, & i f o d d s a r e n e g a t i v e \end{matrix} \\ \begin{matrix} \frac{100}{(o d d s + 100)} * 100 %, & i f o d d s a r e p o s t i v e \end{matrix} \end{matrix}

(2)

Subsequently, the difference in winning probability between the two sides is calculated, thereby constructing the variable WPD_irt as an indicator of perceived skill differences. R _r is a sequence of dummies to control for the variation in effort exertion specific to round r, i.e., the round fixed effects (Brown & Minor, 2014).

In order to test Hypothesis 2 as well as take into account peer effects from teammates on Dota 2 players’ in-game effort choices, a set of variables Sub _imrt are built, corresponding to the above-mentioned nine tactical roles with each measuring the number of additional heroes that can play the identical role on the team. For example, if a player controlling a Disabler hero has two teammates who can fulfill the same role as well, then the value for the related variable is 2. Otherwise, if the hero is the only Disabler on the team or the whole team does not have any Disabler role at all, namely there exist no substitutes, the variable would take the value of 0. Alternatively, this paper capitalizes on a different approach to constructing the Sub _imrt variables. That is, each one takes a dummy form, where its value equals 1 if there is at least one hero in the team with the identical role and 0 otherwise. Such a modification is attempted to check for the robustness of the findings associated with the nine tactical roles.

Data

Player APM and tournament prize data for the current paper were from nine premium Dota 2 tournaments over the 2017-2019 years, including Chongqing, Kuala, and Paris Majors, DreamLeague Season 11, China Supermajor 2018, Epicenter Major 2019, and TIs 7–9. Based on self-written Python web scrapers, the data were collected from three esports-related websites: APM and dead time came from http://www.dotabuff.com; Tournament and hero information came from http://liquipedia.net; and betting odds came from http://www.oddsportal.com. These data were augmented with the rounds and brackets of the matches. The full dataset contains 169 players, 116 heroes, 417 matches, and 4,170 observations in total. Table 1 summarizes the relevant variables analyzed in this paper. APM in the data has a mean of 257.79 and a standard deviation of 102.67. This indicates that the players performed roughly 258 actions every minute on average, and the variable has considerably large variations. The minimum of prize differential is US$28,800 and the maximum is US$2,416,852, meaning the players were allowed to earn at least 28,800 (at most over 2 million) additional US dollars if they could ultimately win the grand prize conditional on which round they were currently situated at. By the same token, the continuum of the relative distribution of prize shows, if winning the final prize, the players could make at least 18% (at most 44%) of the total prize, which ranges from US$1 million to US$34 million.

Table 1.

Summary Statistics for Variables Analyzed in this Study (N = 4170).

Variable	Mean	SD	Min	Max
APM	257.79	102.67	81	605
Deadtime ratio	0.07	0.04	0	0.24
Prize differential	US$632,992	US$857,609	US$28,800	US$2,416,852
Total prize money	US$10,059,827	US$13,064,828	US$1,000,000	US$34,330,068
Relative prize distribution	0.33	0.07	0.18	0.44
Upper bracket	0.36	0.48	0	1
Winning probability difference	0	0.35	−0.82	0.82
Roles
Carry	0.91	1.03	0	4
Nuker	2.34	1.46	0	4
Initiator	0.87	1.07	0	4
Disabler	2.46	1.45	0	4
Durable	0.51	0.85	0	4
Escape	0.65	1.02	0	4
Support	0.58	0.89	0	4
Pusher	0.22	0.56	0	3
Jungler	0.06	0.27	0	2

Note. Roles are the numbers of substitute teammates whose hero can play the identical role.

Results

Table 2 presents estimates for several versions of Equation 1. In addition to control variables, including DTR_imrt, WPD_irt, and the round fixed effects, Model 1 contains the player and hero-specific random effects, the variable of interest PD_rt, the UB_r dummy variable, and the set of variables related to the nine tactical roles. On top of these, Model 2 has an additional interaction term PD_rt*UB_r that is aimed to capture the potential joint effect between the two variables. Standard regression diagnostics including the Wald chi-squared test and the likelihood-ratio test are also provided to help assess the overall significance and the goodness of fit of the models, respectively. It is suggested that the predictor variables in the models are all jointly significant and the random effects models fit the data significantly better than standard regression models without random effects.²

Table 2.

The Incentive Effects of Increased Prize Differentials on Effort Exertion (N = 4170).

	Model 1	Model 2	Model 3	Model 4	Model 5
Constant	252.757***(7.703)	252.926***(7.705)	252.262***(7.469)	248.093***(8.176)	248.376***(8.362)
Deadtime ratio	−2.353***(0.128)	−2.352***(0.128)	−2.361***(0.128)	−2.361***(0.128)	−2.360***(0.128)
Prize differential	5.132***(1.814)	4.160**(1.947)	---	---	---
Total purse	---	---	2.613***(0.892)	---	---
Prize distribution	---	---	---	0.225*(0.125)	0.235(0.147)
Upper bracket	−20.092*** (7.432)	−21.358*** (7.629)	---	−21.544*** (7.402)	−22.999** (11.672)
Prize differential*Upper bracket	---	2.463(3.355)	---	---	---
Prize distribution*Upper bracket	---	---	---	---	0.037 (0.229)
WPD	0.036 (1.834)	−0.014 (1.836)	0.727 (1.732)	−0.035 (1.836)	−0.047 (1.837)
Round fixed effect	Yes	Yes	---	Yes	Yes
Roles
Carry	−1.338 (0.899)	−1.345 (0.899)	−1.366 (0.899)	−1.352 (0.900)	−1.355 (0.900)
Nuker	−0.424 (0.633)	−0.428 (0.633)	−0.339 (0.634)	−0.415 (0.634)	−0.417 (0.634)
Initiator	−0.005 (0.838)	−0.013 (0.838)	−0.070 (0.838)	0.027 (0.839)	0.025 (0.839)
Disabler	1.253 (0.990)	1.255 (0.990)	1.268 (0.991)	1.241 (0.991)	1.241 (0.991)
Durable	1.361 (0.899)	1.356 (0.899)	1.228 (0.900)	1.413 (0.899)	1.412 (0.899)
Escape	−0.963 (0.755)	−0.967 (0.755)	−1.023 (0.755)	−0.976 (0.757)	−0.977 (0.757)
Support	−2.839*** (0.918)	−2.844*** (0.918)	−2.698*** (0.920)	−2.724*** (0.920)	−2.725*** (0.920)
Pusher	1.321 (1.210)	1.289 (1.211)	1.126 (1.211)	1.287 (1.211)	1.282 (1.211)
Jungler	−2.945 (2.197)	−3.001 (2.199)	−3.040 (2.204)	−2.925 (2.199)	−2.937 (2.200)
$σ_{p}$	87.377	87.351	87.294	87.304	87.301
$σ_{h}$	16.710	16.710	16.661	16.737	16.737
$W a l d χ^{2}$	415.80***	416.39***	375.87***	411.34***	411.37***
$d . f .$	22	23	12	22	23
$L R$	8828.28***	8827.43***	8824.03***	8821.54***	8819.30***

Note. Standard errors in parentheses. Prize differential is in millions. WPD = winning probability difference. LR = likelihood ratio.

*** p < 0.01, ** p < 0.05, * p < 0.1.

According to the regression results of Models 1 and 2, the estimated coefficients on DTR_imrt have the predicted negative sign and are statistically different from zero. That is to say, a Dota 2 player whose hero was frequently killed in the game turned out to have a comparatively small value of APM, probably because he lost the control over the hero and had to wait for a while. The coefficient on PD_rt in Model 1 is positive at the 1% significance level, whereas its counterpart in Model 2 has the same sign and similar magnitude, though the level of significance is reduced to 5%. With the inclusion of the interaction term in Model 2, the interpretation of the coefficient on PD_rt has a fundamental alteration. In Model 2, it measures the impact of increased prize differential on players’ effort choice when the corresponding dummy variable takes the value of 0, i.e., competing in the LB. That effect pertinent to UB can be quantified by combining both the coefficients on PD_rt and PD_rt*UB_r. The results indicate that, with an increase of US$1 million in the prize differential, Dota 2 players were projected to improve their exertion of effort by performing 5.132 (Model 1) more APM (roughly 2%) on average, regardless of being in the UB or LB. In Model 2, the estimated coefficient of PD_rt is still significantly positive (β = 4.160, p < 0.05), but that of the interaction term is not statistically significant (β = 2.463, p > 0.1), meaning there existed no substantial behavioral difference between the contestants of UB and LB in putting forth effort responsive to greater prize differentials. Although such a degree of effort improvement is not necessarily impressive in size, the positive sign of the parameter of PD_rt is consistent with Rosen's (1986) predictions pertaining to Hypothesis 1.

The coefficients on UB_r are significantly negative at the 1% level in both models. It is revealed that, ceteris paribus, Dota 2 players reduced effort exertion by performing 20.092 (Model 1) less APM (roughly 8%) on average if provided with a second chance to pursue the grand prize. Coincidently, this finding resonates with Huang's (2016) theoretical analysis on the double-elimination tournament format in the sense that granting a second chance can create asymmetrical motivations with players in the LB being more incentivized than those in the UB. The coefficients on WPD_irt in Models 1 and 2 are small in magnitude and their signs are highly sensitive to the presence of the interaction term, implying that Dota 2 players’ effort choices were not systematically affected by perceived skill differences. However, it should be pointed out that the predictions about the winning side were made for each round rather than for each match. Therefore, players might utilize more recent information they had observed on the field to supplant pregame expectations when updating their beliefs on the probability of winning (Card & Dahl, 2011).

In regards to testing the negative productivity spillovers in the presence of teammates with similar roles, the evidence generally does not support Hypothesis 2. The only exception is the tactical role of Support. The estimated sign and significance of the coefficients on Support are consistent in Models 1 and 2, indicating that Dota 2 players serving the Support role tended to reduce effort by performing 2.839 (Model 1) less APM (roughly 1%) on average with each additional teammate whose hero can play the identical role. Although the slack-off effect associated with the Support role is not sufficiently large in terms of magnitude, this finding helps further the inquiry into team production. Since Support roles are not expected to undertake primary tasks like dealing damages and killing opponents, they are typically dwarfed, in the tactical sense, by other more pronounced roles like Carry and Nuker in the game of Dota 2. Hence, the only evidence from Support roles affirming Hypothesis 2 can be interpreted as that subordinate team members have a stronger propensity to shirk in the presence of teammates with similar roles.

Considering that the incentive effects of tournaments can be attributed to the size (i.e., the inter-tournament effect) and distribution (i.e., the intra-tournament effect) of prize, the variable of interest PD_rt is replaced with the size and relative/percentage distribution of prize money, respectively, in alternative specifications to further determine which factor, or both, contributed to Dota 2 players’ increased effort.³ Models 3–5 in Table 2 displays the results of re-estimating Equation 1 with the two granular components of prize differentials, as well as a new interaction term. In Model 3, it can be seen that the estimated coefficient on total prize money (β = 2.613, p < 0.01) is positive at the 1% significance level, supporting that the overall size of prize was an important contributory factor to the incentive effects of tournaments (Ehrenberg & Bognanno, 1990a, 1990b), namely players choose to put forth more effort as the stakes become higher. On the contrary, the estimation results in Models 4-5 suggest that the incentive effects on effort were not necessarily a result of the prize distribution measured in percentages. The related coefficient in Model 4 (β = 0.225, p < 0.1) is small and only statistically significant at the 10% level, which turns to be insignificant (β = 0.235, p > 0.1) with the inclusion of the interaction term (Model 5). Moreover, the estimated coefficient of the interaction term is not statistically significant (β = 0.037, p > 0.1), indicating no noticeable joint effect between the relative prize distribution and the dummy variable UB_r. As such, the decomposition of the incentive effects of increased prize differentials observed in the main specification suggests that they seem to be more attributed to the total purse of tournaments than the relative distribution of prizes. In Models 3–5, expect for the variables just explained above, the coefficients of the other ones do not differ much from their counterparts in Models 1 and 2.

Last but not least, in an alternative specification where each of the Sub _imrt variables takes the value of 1 if there is at least one hero in the team can serve as the same role and 0 otherwise, the coefficients⁴ of the Support role in all the models remain to be significantly negative. Due to adopting a radically different way to construct the Sub _imrt variables, some of them alter the direction of the coefficient, but their statistical significance does not change much. A discernible change is the coefficient on the Durable role, whose sign switches to significantly negative, meaning Dota 2 players controlling a Durable hero were inclined to reduce effort exertion if at least one of the teammates can fulfill the Durable function. This finding is somewhat intuitive as the tactical purpose of Durable heroes is to absorb damages and protect fragile members, which requires comparatively less APM than other roles like Initiator and Nuker. In the tactical sense, Durable heroes can be thought of as subordinate roles as well. As such, it is reinforced that players in control of subordinate roles are more likely to shirk in esports gaming.

Conclusions

This paper investigates individuals’ effort responses to increased prize differentials based on a direct behavioral metric of effort exertion within the context of esports competition. The analyses of data from nine high-stakes esports tournaments suggest that larger prize differentials stimulate greater effort exertion, providing affirmative empirical evidence to Rosen's (1986) sequential elimination model as well as echoes recent tournament theory-focused findings also derived from the esports setting (Shenkman et al., 2022). Further inquiries uncover that the incentive effects of contests taking the tournament form result largely from the size of the total prize pool in lieu of the relative prize distribution. Also worth noting are the shirking behavior in relation to the double-elimination tournament format (i.e., players are inclined to save effort when having a second chance to continue competing) and the negative productivity spillovers from coworkers (i.e., players with subordinate roles become more likely to slack off in the presence of teammates with similar roles).

Although the incentive effects observed in this paper are significant and robust, they are not necessarily remarkable in magnitude given that a US$1 million increase in prize money is only associated with approximately 2% improvement of effort exertion. This is probably because esports players, like their counterparts in traditional sports, are not solely galvanized by the monetary rewards they face in the short run. First and foremost, sports competitors have an inherent motivation to win, which requires them to spare no effort on the field. As a result, it is difficult for them to further put forth effort by a substantial percentage if they have already tried their best. In addition, winning games is conducive to increasing a player's commercial value and bringing in continued financial benefits (e.g., endorsement deals) beyond what they can earn from the tournaments per se. Therefore, perceived prize money might only play a partial role in determining the competitors’ effort choices.

For future research, the popular esports game Dota 2 can provide a plethora of field data for empirically examining the double-elimination tournament format, the scope of which is still restricted to theoretical analysis (Huang, 2016; Stanton & Williams, 2013) and laboratory experiments (Deck & Kimbrough, 2015). Another direction would be to investigate the relationship between the complementarity of coworkers and their effort choices (Gould & Winter, 2009), which is a topic unexplored in this paper. Finally, the behavioral measure APM can assist labor economists and human resource management researchers in quantifying employees’ effort exertion in today's workplace, where the use of electronic devices such as computers and tablets is ubiquitous.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Eric Mao

Notes

Author Biography

Eric Mao received his Ph.D. degree in Sport and Entertainment Management from the University of South Carolina. He currently works as a lecturer at the School of Cultural Creativity and Management, Communication University of Zhejiang, China.

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