Competition and Coordination in Online Marketplaces

5.1.1. Retailer's Pricing and Channel Selection Decision

If the retailer accepts the marketplace contract, all customers become aware of her channel, that is, all customers become aware of channel b. Thus, when choosing which channel to purchase through, all customers will compare

U b

U B

θ b v − p b ≥ θ B v − p B

θ b v − p b ≥ 0

θ B v − p B ≥ θ b v − p b

θ B v − p B ≥ 0

θ b v − p b < 0

θ B v − p B < 0

p b ≤ θ b

p B ≤ θ B

D b

D B

D b = { 0 , if p B < θ B θ b p b ( p B − p b θ B − θ b − p b θ b ) λ , if p b θ B θ b ≤ p B ≤ p b + θ B − θ b ( 1 − p b θ b ) λ , if p B > p b + θ B − θ b

D B = { ( 1 − p B θ B ) λ , if p B < θ B θ b p b ( 1 − p B − p b θ B − θ b ) λ , if p b θ B θ b ≤ p B ≤ p b + θ B − θ b 0 , if p B > p b + θ B − θ b .

Given these demand functions, we can write the profit function for each channel as

π b = ( p b − c b ) D b

π B = ( 1 − ϕ ) p B D B − k

π A = ϕ p B D B + k

p b

p B

π b + B = π b + π B = ( p b − c b ) D b + ( 1 − ϕ ) p B D B − k .

Theorem 2

If the retailer participates in the marketplace system, with contract parameters k and ϕ, her channel selection decision can be characterized as follows:

If

c b < − ( θ B − θ b ) + θ B ( θ B − θ b )

, then

If

ϕ < 2 c b θ b

, system B0 is optimal

If

2 c b θ b < ϕ < 2 ( θ B − θ b + c b ) 2 θ B − θ b + c b

, system Bb is optimal

If

ϕ > 2 ( θ B − θ b + c b ) 2 θ B − θ b + c b

, system 0b is optimal

If

c b > − ( θ B − θ b ) + θ B ( θ B − θ b )

, then

If

ϕ < 1 − ( θ b − c b ) 2 θ b θ B

, system B0 is optimal.

If

ϕ > 1 − ( θ b − c b ) 2 θ b θ B

, system 0b is optimal.

The optimal prices and profits under each system are as follows.

System B0:

p B = θ B 2

,

π b + B = 1 4 λ ( 1 − ϕ ) θ B − k

, and

π A = k + 1 4 λ ϕ θ B

.

System Bb:

p b = ( 2 − ϕ ) ( 1 − ϕ ) θ b ( θ B − θ b ) + c b [ 2 ( 1 − ϕ ) θ B − ( 2 − ϕ ) θ b ] 4 ( 1 − ϕ ) θ B − ( 2 − ϕ ) 2 θ b p B = 2 ( 1 − ϕ ) ( θ B − θ b ) θ B − ϕ c b θ B 4 ( 1 − ϕ ) θ B − ( 2 − ϕ ) 2 θ b π b + B = [ c b 2 − ϕ c b θ b + ( 1 − ϕ ) θ b ( θ B − θ b ) ] [ 4 ( 1 − ϕ ) θ B − ( 2 − ϕ ) 2 θ b ] · λ ( 1 − ϕ ) θ B θ b − k π A = k + λ ϕ θ B [ ( 2 − ϕ ) ( θ b − c b ) − 2 ( 1 − ϕ ) θ B ] [ ϕ c b − 2 ( 1 − ϕ ) ( θ B − θ b ) ] [ 4 ( 1 − ϕ ) θ B − ( 2 − ϕ ) 2 θ b ] 2 .

System 0b:

p b = 1 2 ( c b + θ b )

,

π b + B = λ ( θ b − c b ) 2 4 θ b − k

, and

π A = k

.

In the above, recall that B0 (0b) denotes a Bb system with no sales on channel b (B).

The retailer's channel selection depends on the interactions between the problem parameters, ϕ,

c b

,

θ B

, and

θ b

. For small values of the retailer's unit cost,

c b

, any of the three outcomes (Bb, B0, and 0b) are possible. As would be expected, when the revenue sharing requirement is minimal (ϕ is small), the B0 system is preferred, as this eliminates the need to pay the unit cost,

c b

. However, when the revenue sharing requirement is significant (ϕ is large), the 0b system is preferred. Finally, when the revenue sharing requirement is moderate, a Bb system is preferred, implying sales through both channels. The results for the case of large

c b

are similar, except that the system with sales through both channels will never be optimal. In general, regardless of the value of

c b

, as ϕ → 0, it becomes optimal for the retailer to have sales only on channel B, whereas, when ϕ → 1, it becomes optimal for the retailer to have sales only on channel b.

The above analysis considers the retailer's decisions under the assumption that she accepts the marketplace contract. In the next section, we consider the question of when it is optimal for the retailer to accept the contract terms and participate in the marketplace program.

5.1.2. Retailer's Marketplace Decision

For a given contract (ϕ,k), the retailer decides whether or not to participate in the marketplace system by comparing the optimal profit. When the marketplace firm offers the marketplace service, he acts as the Stackelberg leader, i.e., he offers the contract with parameters ϕ and k to the retailer, who must then decide whether or not to accept the contract. If the retailer decides not to accept the contract, we assume that the marketplace firm will choose to sell through channel A to obtain some revenues. Therefore, when evaluating the offered contract, the retailer will compare the equilibrium profit obtained from the Ab system, denoted

π b Ab

Theorem 3

The retailer will choose to participate in the marketplace system if and only if the parameters of the marketplace contract satisfy one of the following five sets of conditions:

If

c b < − ( θ B − θ b ) + θ B ( θ B − θ b )

, and:

If

ϕ < 2 c b θ b

and

k < 1 4 λ ( 1 − ϕ ) θ B − π b Ab

,

If

2 c b θ b < ϕ < 2 ( θ B − θ b + c b ) 2 θ B − θ b + c b

and

k < [ c b 2 − ϕ c b θ b + ( 1 − ϕ ) θ b ( θ B − θ b ) ] [ 4 ( 1 − ϕ ) θ B − ( 2 − ϕ ) 2 θ b ] · λ ( 1 − ϕ ) θ B θ b − π b Ab

,

If

ϕ > 2 ( θ B − θ b + c b ) 2 θ B − θ b + c b

and

k < λ ( θ b − c b ) 2 4 θ b − π b Ab

.

If

c b > − ( θ B − θ b ) + θ B ( θ B − θ b )

, and

If

ϕ < 1 − ( θ b − c b ) 2 θ b θ B

and

k < 1 4 λ ( 1 − ϕ ) θ B − π b Ab

.

If

ϕ > 1 − ( θ b − c b ) 2 θ b θ B

and

k < λ ( θ b − c b ) 2 4 θ b − π b Ab

.

These conditions are derived from simple profit comparisons, ensuring that the retailer's profit, if she accepts the marketplace contract, is at least equal to

π b Ab

. One interesting observation from this theorem is that, for certain contract parameters, it would be optimal for the retailer to accept the marketplace contract, but then price such that there are no actual sales through her marketplace channel, i.e., through channel B. In other words, the retailer would offer the product through the marketplace system, but set the marketplace price,

p B

, to ensure that

D B = 0

. The benefit of this approach, for the retailer, is that by participating in the marketplace system, the retailer will expand the set of customers who are aware of her online channel, i.e., who are aware of channel b. Thus, the retailer's total potential market increases from (1 − α)λ, when she sells only through her own channel, to λ when she also participates in the marketplace. In summary, conditions 1c and 2b in Theorem 3 characterize the settings in which it would be optimal for the retailer to pay the fixed fee, k, to participate in the marketplace system, with the goal of expanding the market for her own channel, with no intention of actually selling the product through the marketplace system. As would be expected, this type of behavior is optimal when the level of revenue sharing required for sales in the marketplace system, ϕ, is sufficiently large, whereas the fixed fee, k, is sufficiently small.

5.1.3. Marketplace Firm's Choice of (ϕ,k)

Finally, we consider how the marketplace firm, as the Stackelberg leader, would set the contract parameters, ϕ and k. Notice that, as he does not sell through channel A, the marketplace firm receives zero profit if the retailer chooses not to participate in the marketplace. Thus, the marketplace firm would like to design a contract that will motivate the retailer to join the marketplace. The following theorem presents the marketplace firm's optimal contract parameters:

Theorem 4

If the marketplace firm offers the marketplace service to the retailer, but does not sell the goods himself, the marketplace firm's optimal contract parameters are

ϕ Bb = 0 and k Bb = λ θ B 4 − π b Ab .

The total profit earned by the marketplace firm is

π A Bb = k Bb = λ θ B 4 − π b Ab .

Under the (

k Bb , ϕ Bb

) contract, the retailer will choose to participate in the marketplace and will follow the optimal solution for the B0 system, as given in Theorem 2.

In addition, the (

k Bb , ϕ Bb

) contract maximizes the total system profit,

π A + π b + B

. In other words, the contract coordinates the system in which the marketplace firm does not sell through channel A.

Using the results of Theorem 2, it is easy to verify that if ϕ = 0, then

p B Bb = θ B 2

,

D b Bb = 0

, and

D B Bb = λ 2

. Thus, the optimal profit for the retailer is

π b + B Bb = − k Bb + λ θ B 4 = π b Ab

. While the conditions presented in Theorems 2 and 3 are complex functions of the problem parameters,

c b

,

θ B

, and

θ b

, the overall equilibrium for this system, as specified in Theorem 4, is quite simple and does not depend on the retailer's unit cost,

c b

, other than through the benchmark profit,

π b Ab

.

Notice that the marketplace firm's optimal strategy is to set the contract parameters in such a way as to guarantee retailer's participation in the marketplace, while ensuring that all sales take place through the marketplace system. Also, notice that the marketplace contract achieves channel coordination and, due to its role as Stackelberg leader, the marketplace firm is able to extract all of the retailer's profits in excess of what she would earn in the Ab system.

5.2. Marketplace Firm Sells through Channel A

In this setting, the marketplace firm sells the product through channel A. Thus, there are three channels to consider: A, B, and b. We analyze this three channel system, under the assumption that the marketplace firm offers channel A and wants the retailer to accept the marketplace contract. In section 6, we consider the overall equilibrium, i.e., we determine conditions under which it is optimal for the marketplace firm to offer channel A and to offer the marketplace contract to the retailer.

As we saw in section 5.1, by adjusting the contract parameters, the marketplace firm can manipulate the retailer to sell through any combination of channels B and b. That is, when there are three potential channels, the system can end up in one of three possible outcomes: AB0, A0b, or ABb, where AB0 (A0b) denotes a three channel system with sales only through channels A and B (A and b), whereas ABb denotes a three channel system with sales through all three channels. As the Stackelberg game leader, the marketplace firm is able to select the system that generates the most profit for him. In the following sections, we will analyze each of the three possible outcomes individually. In Section 6, we will use these results, along with those from Sections 4 and 5.1, to determine the overall equilibrium, i.e., to determine which system provides the marketplace firm with the highest overall profit.

5.2.1 AB0 System: Sales through Channels A and B Only

We first consider the system in which the retailer chooses to sell the product through the marketplace system, but not through her own online channel. Thus, as the marketplace firm also sells the product, there are two channels to consider, channel A and channel B. In this system, as the retailer sells through the marketplace system, all customers are aware of both channels. Therefore, when choosing which channel to purchase through, all customers will compare

U A

vs.

U B

, choosing the channel that provides the highest net utility. Thus, if

v − p A ≥ θ B v − p B

and

v − p A ≥ 0

, a customer will choose to purchase through channel A. On the other hand, if

θ B v − p B ≥ v − p A

and

θ B v − p B ≥ 0

, a customer will choose to purchase through channel B. Finally, if

v − p A < 0

and

θ B v − p B < 0

, a customer will choose not to purchase.

Using this logic, assuming that

p B ≤ θ B

, and using the fact that v is uniformly distributed over [0,1], we can write the demand functions for channels A and B,

D A

, and

D B

, as

D A = λ ( 1 − p A − p B 1 − θ B )

and

D B = λ ( p A − p B 1 − θ B − p B θ B )

, where strictly positive demand on each channel requires that the prices satisfy

p B θ B ≤ p A ≤ p B + 1 − θ B

. When any one of these conditions is not satisfied, the AB0 system will transfer to one of the other systems considered in this article. Finally, given the demand functions, we can write the profit function for each channel as

π B = ( 1 − ϕ ) p B D B − k

and

π A = p A D A + ϕ p B D B + k

.

We are now ready to characterize the equilibrium prices and contract parameters for the AB0 system. Recall that the marketplace firm serves as the Stackelberg leader, choosing the contract parameters to optimize his own profits. Also, recall that the retailer will agree to participate in the marketplace system only if her profit under the marketplace contract is at least equal to

π b Ab

. We summarize the AB0 system equilibrium in the following theorem.

Theorem 5

To ensure that the retailer chooses the AB0 system, while maximizing his own profits, the marketplace firm should set the contract parameters as follows:

ϕ AB 0 = 0 and k AB 0 = λ ( 1 − θ B ) θ B ( 4 − 3 θ B ) 2 − π b Ab ,

where

π b Ab

is the retailer's equilibrium profit in the benchmark Ab system. The resulting equilibrium prices and profits are

p A AB 0 = 2 ( 1 − θ B ) 4 − 3 θ B and p b AB 0 = θ B ( 1 − θ B ) 4 − 3 θ B ,

π A AB 0 = λ ( 1 − θ B ) 4 − 3 θ B − π b Ab and π B AB 0 = π b Ab .

The theorem says that to ensure that the retailer chooses the AB0 system, the marketplace firm should set ϕ = 0, i.e., the marketplace contract should have no revenue sharing. This, coupled with the fact that the unit cost of selling through channel b is

c b > 0

, implies that the retailer has no incentive to offer the product through channel b. In addition, the theorem indicates that the marketplace firm is able to extract all profits in excess of the benchmark profit (

π b Ab

) from the retailer.

5.2.2. A0b System: Sales through Channels A and b Only

We next consider the system in which the retailer chooses to participate in the marketplace system, but with sales occurring only through her own online channel. Thus, there are two channels with positive sales, A and b. Recall that by participating in the marketplace system the retailer is able to increase her potential market from (1 − α)λ to λ. Thus, there may be instances in which the retailer would find it beneficial to pay the fixed cost, k, to participate in the marketplace system, even if she will not have any actual sales through channel B.

When making their purchasing choice, all customers will compare the net utilities offered by channels A and b. Using the same logic as applied in the previous sections, assuming that

p b ≤ θ b

, and using the fact that v is uniformly distributed over [0,1], we can write the demand functions for channels A and b,

D A

and

D b

, as

D A = λ ( 1 − p A − p b 1 − θ b )

and

D b = λ ( p A − p b 1 − θ b − p b θ b )

, where strictly positive demand on channels A and b requires that the prices satisfy the following conditions:

p b θ b < p A ≤ p B + ( p B − p b θ B − θ b ) ( 1 − θ B ) and p A − p b 1 − θ b ≤ 1 .

When any one of the above conditions is not satisfied, the A0b system will transfer to one of the other systems considered in this article. Finally, given these demand functions, we can write the profit function for each channel as

π b = ( p b − c b ) D b − k

and

π A = p A D A + k

.

We are now ready to characterize the equilibrium prices and contract parameters for the A0b system. We do so in the following theorem.

Theorem 6

If

c b < 2 θ b ( 1 − θ b ) 4 − 3 θ b

, to ensure that the retailer chooses the A0b system, while maximizing his own profits, the marketplace firm should set the contract parameters as follows:

ϕ A 0 b = 1 and k A 0 b = λ [ c b 4 θ b ( 1 − θ b ) − θ b ( 1 − θ b ) ( 4 − 3 θ b ) 2 ] − π b Ab ,

where

π b Ab

is the retailer's equilibrium profit in the benchmark Ab system. The resulting equilibrium prices and profits are

p A A 0 b = 2 ( 1 − θ b ) 4 − 3 θ b and p b A 0 b = c b 2 + θ b ( 1 − θ b ) 4 − 3 θ b ,

π A A 0 b = λ [ c b 2 ( 4 − 3 θ b ) + 4 ( 1 − θ b ) 2 θ b 4 θ b ( 1 − θ b ) ( 4 − 3 θ b ) ] − π b Ab and π B A 0 b = π b Ab .

The condition

c b < 2 θ b ( 1 − θ b ) 4 − 3 θ b

is required to ensure that the conditions stated in Eq. (1), which imply positive demand on channels A and b, hold. The theorem says that, to ensure that the retailer chooses the A0b system, the marketplace firm should set ϕ = 1, i.e., the marketplace contract should require 100% revenue sharing. This, of course, implies that the retailer has no incentive to offer the product through channel B. This result is in contrast with the results presented in Theorems 4 and 5, in which the optimal ϕ is set to zero. Note that in the systems considered in those theorems (the Bb and AB0 systems), the marketplace firm was trying to encourage sales through channel B. Thus, setting ϕ = 0 for these cases makes intuitive sense. Finally, the theorem indicates that the marketplace firm is able to extract all profits in excess of the benchmark profit (

π b Ab

) from the retailer.

5.2.3. ABb System: Sales through Channels A, B and b

Finally, we consider the system in which the retailer chooses to sell the product through the marketplace system, as well as through her own online channel. Thus, there are three channels to consider: channel A, channel B, and channel b. In this system, as the retailer sells through the marketplace system, all customers are aware of three channels. Therefore, when choosing which channel to purchase through, all customers will compare

U A

vs.

U B

vs.

U b

, choosing the channel that provides the highest net utility. Using the same logic as applied to the previous cases, assuming that

p B ≤ θ B

,

p b ≤ θ b

, and

p B θ B ≥ p b θ b

, where the last condition is required to ensure that there is potential for

D b > 0

, and using the fact that v is uniformly distributed over [0,1], we can write the demands for channels A, B and b,

D A

,

D B

, and

D b

, as follows:

D A = λ ( 1 − p A − p B 1 − θ B ) , D B = λ ( p A − p B 1 − θ B − p B − p b θ B − θ b ) , and D b = λ ( p B − p b θ B − θ b − p b θ b )

To ensure positive demand on all three channels, we require the prices to satisfy the following conditions:

p A > p B + ( p B − p b θ B − θ b ) ( 1 − θ B )

and

p A − p B 1 − θ B ≤ 1

.

We can now write the profit functions for each channel as

π A = p A D A + ϕ p B D B + k

,

π B = ( 1 − ϕ ) p B D B − k

, and

π b = ( p b − c ) D b

. As the retailer owns both channel b and channel B, she will choose

p b

and

p B

to maximize

π b + B = π b + π B = ( p b − c ) D b + ( 1 − ϕ ) p B D B − k

, whereas the marketplace firm will choose

p A

, ϕ, and k to maximize

π A

.

We are now ready to state our main result for this three channel case:

Theorem 7

No equilibrium with strictly positive demand on all three channels exists for the ABb system.

We prove Theorem 7 by demonstrating that, in the ABb system, the marketplace firm will choose to set the revenue sharing parameter, ϕ, so that there are no sales on channel B. The intuition behind this result is that, when there are positive demands on channels b and B, to maximize his profits, the marketplace firm will take a large portion of the revenue earned on channel B, i.e., ϕ will be large. In contrast, when ϕ is large, the retailer will find it optimal to forgo the potential revenue from channel B, and will instead set

p B

very high, so that no sales occur on channel B. In this way, the retailer shifts demand from channel B to channel b, where the retailer is able to keep all of the revenue.

6. Analysis of Overall System Equilibrium

Our goal is to characterize the overall system equilibrium, i.e., to determine whether the marketplace firm will offer the marketplace contract to the retailer, to determine whether the marketplace firm will choose to sell the product through channel A and at what price, and to characterize the retailer's channel selection and pricing decisions. Before doing so, we summarize the analysis completed so far.

We considered the case in which the marketplace firm chooses not to offer the marketplace service. We analyzed this Ab system to determine the equilibrium prices and profits.

We then considered the case in which the marketplace firm chooses to offer the marketplace service. There were two subcases to consider:

○

The case in which the marketplace firm does not offer the product through channel A and thus only channels B and b exist. For this system, we demonstrated that the marketplace firm, as Stackelberg leader, will set the contract parameters such that the overall equilibrium has sales only through channel B. Thus, the resulting equilibrium is the B0 system.

○

The case in which the marketplace firm offers the product through channel A, and thus, all three channels (A, B, and b) exist. For this system, a retailer who participates in the marketplace system has three options: ○

Sales through B only, the AB0 system

○

Sales through b only, the A0b system

○

Sales though both B and b, the ABb system

We analyzed the marketplace firm's optimal contract design for each of these three cases, and demonstrated that no equilibrium exists for the ABb system.

Thus, to determine the overall system equilibrium, we must compare four systems: Ab, B0, AB0, and A0b. In section 6.1, we present our results regarding this comparison and mathematically characterize the conditions under which each of these systems will be the overall equilibrium. Then, in Section 6.2, we provide some intuition behind these results and present some numerical results.

6.1. Characterizing the Overall System Equilibrium

As the marketplace firm is the Stackelberg leader, it is able to select his preferred system from among these four potential equilibrium systems (Ab, B0, AB0, and A0b) by adjusting the parameter values of the contract. Thus, by comparing the four systems, we just need to consider the marketplace firm's profits and find the system that provides the highest profits. The results for the four systems are summarized in Table 1. Notice that, for ease of comparison, we have rewritten the expression for

π A Ab

, as given in Theorem 1, so that we can compare the profit functions by considering only the first term of each, ignoring the

π b Ab

term. Clearly, the relationship between the profits for the four systems depends on the specific parameter values. However, it is possible to draw some conclusions regarding which system will be the overall equilibrium under a range of possible parameter values, as shown in the following theorem.

OPEN IN VIEWER

Table 1

Potential Equilibrium Systems

System	Conditions Required for Existence of an Equilibrium	Marketplace Firm's Profit at Equilibrium
B0	None	λ ( θ B 4 ) − π b Ab
Ab	c b < ( 1 − θ b ) θ b 2 − ( 1 + α ) θ b	λ ( [ 2 + ( 1 − α ) c b − 2 θ b ] 2 θ b ( 1 − α θ b ) + ( 1 − α ) [ θ b − θ b 2 − c b ( 2 − ( 1 + α ) θ b ) ] 2 θ b ( 1 − θ b ) [ 4 − ( 1 + 3 α ) θ b ] 2 ) − π b Ab
	θ b < 4 2 + 4 − 3 α + 3 α
AB0	None	λ ( 1 − θ B 4 − 3 θ B ) − π b Ab
A0b	c b < 2 θ b ( 1 − θ b ) 4 − 3 θ b	λ [ c b 2 ( 4 − 3 θ b ) + 4 ( 1 − θ b ) 2 θ b 4 θ b ( 1 − θ b ) ( 4 − 3 θ b ) ] − π b Ab

Theorem 8

There exist a series of thresholds whose precise definitions are provided in the proof of this theorem, such that the overall equilibrium can be determined as followed:

If all four system equilibria exist according to the conditions specified in Table 1, then use the logic shown in Figure 2.

If only the AB0, B0, and A0b system equilibria exist according to the conditions specified in Table 1, then use the logic shown in Figure 5 in the Online Appendix.

If only the AB0, B0, and Ab system equilibria exist according to the conditions specified in Table 1, then use the logic shown in Figure 6 in the Online Appendix.

If only the AB0 and B0 system equilibria exist according to the conditions specified in Table 1, then AB0 is the overall equilibrium if

θ B < 2 3

. Otherwise, B0 is the overall equilibrium.

OPEN IN VIEWER

Figure 2

Overall System Equilibrium: All Systems (AB0, B0, A0b, and Ab) Exist

The tree shown in Figure 2 can be used to determine which of the systems is the overall equilibrium for any given set of parameter values. In the tree, we use the > symbol to denote when one system dominates the other, in terms of the total system profit.

6.2. Discussion and Numerical Results

We will focus our discussion of these results on the tree shown in Figure 2, which applies in settings in which an equilibrium exists for all four potential systems (B0, AB0, A0b and Ab). In this tree, we start by comparing the three systems in which the retailer agrees to the marketplace contract, i.e., B0, AB0, and A0b, to determine which is preferred by the marketplace firm. Once we have determined the best of these three systems, that best system is then compared with the “pure competition” system, i.e., Ab, in which the marketplace firm does not offer the marketplace contract, and thus enters into a purely competitive relationship with the retailer.

We start by discussing the first node in the tree, in which the marketplace firm chooses among B0, AB0, and A0b. We first note that AB0 is never selected by the marketplace firm in this setting. As shown in the proof of the theorem, this is due to the fact that the marketplace firm always prefers A0b to AB0. In other words, given that the retailer agrees to the marketplace contract and that the marketplace firm chooses to sell through channel A, the marketplace firm prefers to compete against channel b, than against channel B. This is because channel b can be considered to be a weaker competitor than channel B due to its higher unit cost (

c b > 0

) and lower overall utility (

θ b < θ B

). Next, we consider the retailer's preference for B0 vs. A0b. Three conditions must hold for the B0 system to be preferred over the A0b system:

θ B

and

θ b

must be sufficiently large (

θ B > 2 3

and

θ b > θ ˜ b

), whereas

c b

must be sufficiently small (

c b < c ̂ b

). Having a large

θ b

and a small

c b

implies that channel b is a strong competitor, and thus the A0b system may not be highly profitable for the marketplace firm. In addition, when

θ B

is large, selling through channel B is attractive for the marketplace firm, as that firm extracts all of the retailer's excess profits (beyond those earned in the Ab system). Finally, as would be expected, if

θ B

is sufficiently small (

θ B < 2 3

), regardless of the other parameter values, the A0b system will be preferred to the B0 system.

We next consider the remaining two nodes in the tree, in which we compare the best system from the first node (B0 or A0b) with the pure competition system, Ab. In the top part of the tree, we compare A0b and Ab. The marketplace firm's choice between these systems depends on the value of α, the fraction of customers who are not aware of channel b when the retailer does not sell through the marketplace system. When α is small, i.e.,

α < α ˜

, the A0b system is preferred. On the other hand, when α is large, i.e.,

α > α ˜

, the Ab system is preferred. The intuition behind this result is provided in the discussion of Figures 3 and 4 below. In the bottom part of the tree, we compare B0 and Ab. We see that B0 is preferred only when the utility obtained by purchasing through channel B,

θ B

, is sufficiently large (

θ B > θ ̂ B

), and the unit cost associated with channel b is sufficiently small (

c b < c ¯ b

).

OPEN IN VIEWER

Figure 3

Overall System Equilibrium as a Function of α and

c b

OPEN IN VIEWER

Figure 4

Overall System Equilibrium as a Function of

θ b

and

c b

Figures 3 and 4 are contour graphs, i.e., they were created by comparing the profits for each system. Each region's label represents the system preferred by the marketplace firm and the lines represent the thresholds shown in Figure 2. In Figures 3a and 4a, we have

θ B > 2 / 3

, and thus the figure shows how the marketplace firm chooses between the A0b, Ab, and B0 systems. Figure 3a demonstrates that when the unit cost for sales on channel b (

c b

) and the fraction of customers who are not aware of channel b (α) are sufficiently small, channel b is seen as a strong competitor, and thus, the B0 system is preferred over both the A0b and Ab systems. In the remainder of the graph, the marketplace firm faces a choice between the A0b and Ab systems.

In the A0b system, all customers are aware of channel b, whereas in the Ab system, a fraction (α) of customers are not aware of channel b. Thus, the A0b system provides the retailer with a larger market share and creates a higher level of competition for the marketplace firm.

In the A0b system, the marketplace firm uses the marketplace contract to extract all excess profits (beyond those earned in the Ab system) from the retailer.

Intuitively, (1) makes the A0b system less attractive to the marketplace firm, whereas (2) makes the A0b system more attractive to the marketplace firm. When α is small, the effect of (1) is minimal, and thus (2) dominates, making the A0b system attractive to the marketplace firm. If α is large, but

c b

is also sufficiently large, then channel b is a weak competitor (observe that a high unit cost on channel b will imply a high unit price on channel b). Thus, the effect of (1) is again minimal, i.e., even a substantial increase in the retailer's market share will not hurt the marketplace firm very much, allowing (2) to dominate, and making the A0b system attractive to the marketplace firm.

Figure 4a can be interpreted in a similar manner. When channel b is seen as a strong competitor (sufficiently small unit cost,

c b

, and large utility,

θ b

), the B0 system is preferred over both the A0b and Ab systems. On the other hand, when the utility associated with channel b (

θ b

), is sufficiently low, the marketplace firm would prefer to compete with channel b, rather than channel B. Thus, the choice is between the A0b and the Ab systems. Using the same logic as applied to Figure 3a, we find that the A0b system is preferred only when the unit cost for channel b is sufficiently high, allowing the effect of (2) to dominate over the effect of (1).

Figures 3b and 4b can be understood by noting that

θ B < 2 / 3

, and thus the B0 system is never the overall equilibrium. Recall that in the B0 system, the marketplace firm extracts all of the retailer's excess profits. When the utility associated with purchasing on channel B is sufficiently low (

θ B < 2 / 3

), these excess profits will not be sufficient for the marketplace firm to justify not selling through channel A. Thus, Figures 3b and 4b show the marketplace firm's choice between A0b and Ab. This choice can again be explained by considering the trade‐off between (1) and (2). When α is sufficiently small or

c b

is sufficiently large, the effect of (2) will dominate the effect of (1), and the marketplace firm will choose the A0b system.

In summary, there are three possible equilibria, representing different degrees of coordination and competition between the marketplace firm and the retailer, as outlined below:

Pure Coordination (System B0): Sales in this system only take place through channel B, with the retailer and the marketplace firm sharing the overall profits. This system will be the equilibrium when the retailer is a sufficiently strong competitor, i.e., when the utilities associated with channels B and b are sufficiently high and the unit cost for channel b is sufficiently low.

Pure Competition (System Ab): The marketplace firm does not offer the marketplace contract, and thus, enters into a purely competitive relationship with the retailer's online channel. This case will be the equilibrium when the retailer is viewed as a weak competitor to the marketplace firm, i.e., if the utility associated with either of the retailer's channels (B and/or b) is sufficiently low or if the fraction of customers who do not know about the retailer's online channel is large.

Competition and Coordination (System A0b): In this system, the marketplace firm and the retailer simultaneously coordinate (the retailer agrees to the marketplace contract) and compete (the retailer sells through her own channel). This case is preferred to pure competition only when allowing the retailer to be visible to all customers poses a minimal threat to the marketplace firm's own sales through the marketplace system. This case is preferred to pure coordination except in settings in which the retailer's channels (B and b) are viewed favorably by customers (have a low disutility) and the retailer's unit cost for sales on her own channel is small.

Finally, while we will not discuss the trees shown in Figures 5 and 6 the Online Appendix, which apply in settings in which one or more of the systems does not have a feasible equilibrium solution, we note that the results can be explained using the same logic used to explain the tree in Figure 2. However, there is one additional result worth noting. As noted in the final bullet of Theorem 8, when neither the A0b nor the Ab systems have a feasible equilibrium, it is possible that the AB0 system will be the overall equilibrium. However, this will only occur when

θ B

is sufficiently small, i.e., when

θ B < 2 3

, the AB0 system will be preferred over the B0 system.

7. Managerial Insights and Conclusions

In this article, we consider a setting in which a marketplace firm, such as Amazon, operates an online marketplace through which retailers can sell their products directly to consumers. We consider the question of under what conditions an online retailer would choose to contract with the marketplace firm to sell its product through the marketplace system. Selling the product through the marketplace expands the market of available customers for the retailer, but also comes at a cost, i.e., a fixed participation fee plus revenue sharing. We also consider the problem from the perspective of the marketplace firm, studying how the firm would decide whether or not to offer the marketplace contract to the retailer, how the firm would set the marketplace contract parameters, and whether the marketplace firm would choose to sell a competing product through the marketplace system.

This research was inspired by the experience of companies such as Ice.com, who are initially motivated to join the marketplace system to access a larger segment of customers, but who later find that they must compete directly with the marketplace firm, and thus must confront the question of whether to continue selling through the marketplace system. The results of our research indicate that the situation Ice.com found itself in during 2004, with sales of its goods occurring through both its own online store and through the Amazon marketplace, the latter in direct competition with similar products being sold by Amazon, may not be a stable one. In other words, we find that the three channel system will not exist in equilibrium. Instead, the equilibrium will be one of four types, all of which have sales through only two channels. We summarize each of these possibilities below:

In the pure coordination equilibrium, the retailer agrees to participate in the marketplace contract, while the marketplace firm chooses not to sell the product itself. The retailer sets the prices in such a way that there is no demand through her own online channel, i.e., sales occur only through her marketplace channel. The marketplace firm sets the contract parameters, i.e., the fixed payment and degree of revenue sharing to coordinate the system, i.e., to maximize total profit for the system, while extracting as much profit from the retailer as possible, making the retailer indifferent between participating in the marketplace system and not participating.

In the pure competition equilibrium, on the other hand, the retailer does not participate in the marketplace system. Instead, the retailer's online store and the marketplace firm coexist and compete for a portion of the market, each setting their own prices to maximize their own profits. In this system, as there is no contract between the retailer and the marketplace firm, the total system profit is unlikely to be maximized, i.e., the system is not coordinated.

In the competition and coordination equilibria, the marketplace firm and the retailer simultaneously coordinate (the retailer agrees to the marketplace contract) and compete (the retailer sells through either her own channel or through the marketplace system, but not both).

We have also characterized the conditions under which each of these systems is likely to be the equilibrium. First recall that, as the Stackelberg leader, it is the marketplace firm who, in the end, determines which equilibrium will result, i.e., the overall system equilibrium will be whichever system provides the marketplace firm with the highest profits. We find that the pure competition equilibrium becomes more likely when the retailer is seen as a weak competitor to the marketplace firm (i.e., the retailer has low name recognition or low utility). In other words, if the marketplace system is viewed as being more secure or as providing a greater level of service than the retailer, and thus consumers have a clear preference for engaging in transactions with the marketplace firm rather than with the retailer, then the competitive equilibrium is more likely. On the other hand, we find that the pure coordination equilibrium becomes more likely when consumers do not have a strong preference for purchasing from the marketplace system relative to purchasing from the retailer, i.e., when the utilities gained from purchasing through either of the retailer's channels are large, and when the retailer's unit cost is low. In particular, as the utility associated with purchasing through the retailer's online store increases, getting closer to the utility obtained from purchasing through the marketplace firm, the two channels become more competitive, and the profits earned by the marketplace firm in the competitive equilibrium decrease, making the coordinated equilibrium more attractive.

Finally, this article contributes to the existing literature by studying a specific form of channel conflict created by an Amazon‐type marketplace system. Specifically, we study the impact of competition in an online marketplace system in which the marketplace firm both designs the marketplace contract with the retailer and, potentially, sells a product that directly competes with the good sold by the retailer. In such a system, the relationship between the marketplace firm and the retailer is both horizontal and vertical. In addition, the marketplace firm is the dominant partner in the system due to its name recognition, as well as its role as owner of the marketplace system. We believe we are the first to study this particular form of channel conflict and to understand the potential equilibrium outcomes for such a system. Given the rapid growth of such marketplace systems, understanding the impact of competition and channel conflict in these systems is of critical importance to the success of marketplace firms such as Amazon, as well as the retailers who take part in these systems.

7.1. Limitations and Future Research

We conclude this article with a discussion of several limitations of our current model. First, as noted above, we assume that both marketplace channels (B and A) have the same unit cost, and we normalize these costs to zero, leaving only the unit cost,

c b

, for channel b. In reality, it may be the case that the marginal costs on channels A and B will be different, i.e., we might expect that

c A < c B < c b

. Unfortunately, incorporating additional unit costs into the model makes the analysis extraordinarily complex. However, we can use the results from the current analysis to draw some conclusions regarding the impact of marginal costs for the marketplace channels on the equilibrium results. For example, if we had a positive marginal cost on channel B, i.e.,

c B > 0

, a higher unit cost would make channel B less competitive, thus making it more likely that the marketplace firm would be willing to compete directly with channel B, i.e., making it more likely that the marketplace firm would select the AB0 system as the overall equilibrium. Having a higher value of

c B

would also make it less likely that the overall equilibrium will have sales only through channel B, i.e., the B0 system, as having a higher

c B

makes channel B less profitable, implying that the marketplace firm would earn less through revenue sharing in the B0 system. Future research will seek to formalize this intuition.

Next, we note several other limitations of our model setting. First, while we have assumed a certain sequence of decisions in our problem setting, other sequences are possible. Specifically, we have assumed that the marketplace firm, as the Stackelberg leader, acts first and sets the contract parameters, ϕ and k, as well as his selling price,

p A

. The retailer then simply reacts to these decisions by the marketplace firm and sets her price(s). However, it is very possible that the marketplace firm would seek to set its price after the retailer sets her price(s). In this case, the sequence of decisions would be a bit more complex, with the marketplace firm first setting ϕ and k, the retailer then setting her price(s), and finally the marketplace firm setting its price. Investigating this alternative decision sequence, to understand how it affects the equilibrium results, would be an interesting topic for future research. Second, we have not captured the dynamic nature of the relationship between the retailer and the marketplace firm. This would be an important extension to consider, particularly in settings in which participation in the marketplace system is likely to affect consumers' views of the retailer, i.e., as time goes by, one would expect that more and more consumers will become familiar with (and possibly more trusting of) the retailer, implying that α may decrease over time, whereas the utility associated with purchases through the retailer may increase. Such changes may lead the marketplace firm to adjust the contractual relationship with the retailer over time. Third, we could also extend the model to consider several retailers participating in a single marketplace system. In this case, a retailer's decision regarding whether or not to sell their product on the marketplace will be affected by the level of competition in the marketplace (i.e., the number of retailers), as well as the degree of similarity between the products (i.e., the relative values of the

θ i

across the retailers). Also, in such a setting, the competition between the retailers would need to be modeled using a Nash game. Finally, a related extension would be to consider the role of product complementarity, i.e., the fact that the market size for the marketplace firm is dependent on the variety of products offered on the marketplace system, with more variety associated with a larger market. In such a setting, the marketplace firm may choose to offer more attractive contractual terms to those retailers who offer products that are not currently being sold on the marketplace system.

Footnotes

Acknowledgments

The authors thank the departmental editor (Professor Amiya K. Chakravarty), senior editor, and two referees for their contribution in improving the clarity and quality of this paper.

1

Author names are listed alphabetically and all authors contributed equally.

2

http://advantage.amazon.com/gp/vendor/public/faq#marketplaceDiff

3

http://www.amazonservices.com/promerchant>ld=AZSOAMakeM

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