# Intra Platform Competition In Two Sided Markets Economics Essay

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## Introduction

This paper addresses the issue of intra-platform competition in two sided markets. Two sided markets are defined as markets where two 'consumer' groups interact through intermediaries/platforms. A few examples of two-sided markets are malls (retailers interact with consumers), operating systems (application-based software developers with users) and media (advertisers with users). In each of these cases, one group interacts with the other through the platform, and the platform can extract profits out of these groups.

The model developed looks at the optimal competition on one side of the market that a platform should allow in order to maximise profits. There are two opposing forces that the platform faces. If the platform restricts competition, then, it can obtain a huge payout from the monopolist. On the other hand, if it allows competition, then, the other side of the market benefits from this competition, and the platform can extract a surplus from this side of the market. The platform's decision depends on these forces.

The rest of this paper is structured as follows. In Section II, some distinctive features of two-sided markets and conditions for its existence in light of the Coase Theorem are discussed. Section III is a review of the existing literature on pricing and competition in two-sided markets, focussing on three papers, one by Rochet and Tirole (2003) on pricing, one by Armstrong (2006) on intra-platform competition with Bertrand pricing, and one by Dukes and Gal-Or (2003). Section IV outlines a more comprehensive model for this problem, by extending the Armstrong (2006) model, which incorporates Cournot competition between the firms, and allows for a larger range of services on one side of the market. Section V compares the results of the model with the evidence. The final section concludes a few remarks on the assumptions of the model.

## II

## Two-Sided Markets: An Overview

As mentioned before, in two-sided markets, there are two groups that benefit from using a product, and gain more if more of the other group uses the same product. Specifically, these are markets with 'cross-group externalities', i.e. the payoff to one group depends on the number of agents in the other group on the same platform.

Let us briefly discuss the three main features that characterise a two-sided market:

Externalities: Each group's utility depends on the number of users from the other group using the platform. However, if one group gains very strongly from more users from the other group, then, the platform could subsidize the other group to attract a larger number of the first group and extract a larger surplus from this group. Rochet and Tirole (2003) classify the nature of externalities into (i) the more common usage externalities (externalities generated only on use) and (ii) the less common membership externalities (externality generated by merely joining the platform).

Homing: Users in the groups might use only one platform, or use multiple platforms. This determines the extent of externalities, and the price elasticity within the platform. There are three possible combinations based on homing; both groups single-home, one group single homes while the other multi-homes and where both groups multi-home.

Pricing: Using Tirole and Rochet (2006), the charges levied by the platform could either be a fixed membership charge or a usage charge. This would depend on the nature of externalities, and the bargaining power of the platform. Often, one side of the market is loss-making or heavily subsidized while the other side is the profit making stream. For example, in the case of software platforms, the viewers/users are subsidized while the servers/content developers are the source of profits. Similarly, in media, the viewers are subsidized while the advertisers are the source of revenues.

## Failure of the Coase Theorem

This sub-section discusses the conditions that are necessary for the existence of two-sided markets and draws largely from the discussion in Rochet and Tirole (2006). According to the Coase theorem, in the absence of transaction costs and information asymmetry, and if property rights are established and can be traded, then, negotiation between agents would lead to an efficient outcome in the presence of externalities.

According to the theorem, if there is a platform that acts as an intermediary between the two groups of agents, the gains from trade depend only on the price levels and not the allocations. Moreover, the allocation has no impact on the volume of transactions, the platform's profits or social welfare, thereby causing the markets to be one-sided. That is, the platform merely acts to reduce transaction costs, and makes the theorem applicable.

Failure of the Coase theorem is a necessary but not sufficient condition for the existence of two-sided markets.

To illustrate the above argument, consider the failure of the theorem due to asymmetric information. Asymmetric information causes inefficient outcomes in negotiations as each party bargains for more than what the other party can give. The market, however, remains one-sided. Thus, the failure of the Coase theorem does not imply two-sidedness.

## III

## Literature Review

Until 2003, the literature on two-sided markets was scant. Most of the analysis of these industries either focussed on network economics or on multi-product pricing. Since, there have been several papers that have looked at two-sided markets. A brief summary of the important contributions relevant to the industry follows. Three models that are relevant to this paper are outlined in greater detail in the following subsection.

Some of the best overviews of two-sided markets are obtained from Rochet and Tirole (2003, 2006) and Evans (2003). The early literature on two-sided markets assumes a monopoly platform and exogenous homing. Subsequent literature has relaxed this assumption and several papers have considered the case of competing platforms. Caillaud and Jullien (2003) consider cases where there is no product differentiation between the two platforms while Armstrong (2006) considers the case where there is strong product differentiation on both sides of the market. Armstrong and Wright (2007) consider an intermediate case where one side of the platform views the platforms as homogenous and the other side does not. They arrive at different conclusions on the nature of pricing and on welfare implications. On the homing side, Roson (2005) builds a model of two-sided markets that makes homing endogenous. He argues that low net benefits that are independent of the transactions reduce the likelihood of multi-homing. Platform competition, while it creates a downward pressure on prices, has an ambiguous effect on the homing decision.

Stahl (1982) develops a simple model where firms supplying substitutes might find location on the same platform, that is, in spite of increased competition, prices are not driven down to zero. His argument proceeds as follows. Consumers are offered a choice between a smaller platform, and a larger one. The larger one offers a wider range of products. These may be substitutes or complements. Consumers choose the platform that offers the lowest price-distance combination, and prefer a wider choice. Firms on the same platform exhibit Nash-Cournot competition in prices. These preferences would lead competing firms to locate on the same platform in spite of the fact that this would push prices down. He also shows that the Cournot oligopolists could charge a higher price than monopoly firms located at different points, if their products are not 'too close substitutes'. This is because to the consumer, the disutility because of the higher prices is outweighed by a larger choice and lower transport costs.

In this sub-section, three models relevant to the topic are discussed in greater detail. The Rochet and Tirole model (2003) of credit card markets examines the price structure under different platform regimes, i.e. a monopoly platform which maximises profits, a monopoly platform that maximizes social welfare and a duopoly platform. This model allows for price heterogeneity and the dependence of price on elasticity, which is very similar to the results developed in Section IV. The second and third models are by and Dukes and Gal-Or (2003) and by Armstrong (2006) respectively, which look at intra-platform competition. The Dukes and Gal-Or model is specifically for advertising, where the consumers' utility from the platform decreases with an increase in advertising. Finally, the Armstrong paper is the inspiration for the more comprehensive model of Section IV.

Inter-Platform Competition

Rochet and Tirole (2003) model the credit card market. They consider the case where there are no fixed charges, and both sides are charges on a usage basis and assume multi-homing, with multiplicative demand and a symmetric equilibrium. They argue that the pricing decision of a monopoly platform follows the following rules:

Price formula:

where p is the price, c the cost and η the elasticity of demand

The price allocation rule:

where, pB,pS, ηB, ηS are the prices and elasticities of buyers and sellers repectively, and p= pB+pS, η= ηB+ηS and c is the marginal cost.

A Ramsey planner on the other hand will set prices on the basis of the following rules:

1. Price/Budget formula: c= p= pB+pS

2. Cost/Price Allocation:

Where, VB and VS are the total utilities of the two sides of the markets, defined by

where Dk is the demand for k=B,S

The Ramsey model takes into account the surplus generated by getting more end users on one side. However, for some demand formulations, for example, the linear demand case, there is no price bias.

In the case of competing platforms, a symmetric equilibrium would be

This differs from the monopoly problem in that > ηB is the own-elasticity of demand, and is replaced by an 'own-brand elasticity' term , where σ is the level of homing. For the single homing case, σ =1, and decreases as multi-homing increases. It can be seen that an increase in multi-homing would reduce σ, and in equilibrium, lead to a lower pS, that is lower prices for the seller. Therefore, multi-homing on one side reduces the price for the other side.

To summarize their argument, the pricing distribution depends on relative elasticities, irrespective of the extent of platform competition or the governance structure of the platform. To use the credit card metaphor, if consumers view credit cards as close substitutes, then, they would bear a lower fraction of the prices as compared to the credit card companies. The extent of substitutability depends on whether retailers would be willing to accept only one card or multiple cards.

Intra-platform Competition in Advertising:

Dukes and Gal-Or (2003) develop a similar model for advertising. They consider differentiated media platforms courting differentiated advertisers. The media platforms bargain with advertisers for a fixed payment, subsequent to which they broadcast advertisements. They show that the level of advertising increases with the diversity of media platforms but is independent of the differentiation between the advertisers' products. They also show that both parties are worse off at higher levels of differentiation which causes high advertising and therefore tougher price competition in the end market. With exclusivity contracts, the advertiser, facing less competition in the end market, reduces the level of advertising. They model the exclusivity arrangements in the form of a bargaining outcome between the platform and the advertiser.

In the model, the platforms and the advertisers are non-homogenous, the preferences of the consumer over the two are independent, and consumers are distributed evenly on a unit line. There are two producers (i=1,2) and two stations located at either end of the Hotelling line. The producers bear a fixed cost k and a cost of c per unit. The platform bears a fixed cost f.

The two stage game has the following stages. In stage 1, the platform and the advertisers negotiate the price for advertising, aji, the advertiser chooses the level of advertising and the price it can charge consumers, pi. The negotiation is modelled as a Nash-bargaining game and the price setting is assumed to be sequential in a restricted sense. In stage 2, the consumer decides on viewing behaviour based on the utility function as described below.

Consumers obtain a utility vp from consuming the product, and a utility vs from the media platform, and their utility declines at a rate of tp and ts respectively with the distance from the product or the platform. The consumer's utility from the platform also declines with the aggregate level of advertising Θj=φ1+φ2. The utility function from viewing platform j has the form,

where, x is the distance of the consumer from the platform. Utility is derived from viewing one particular platform over a period of time and is independent of distribution of advertisers on a platform. Therefore the market share of platform j is given by,

The market share declines with additional ads on the same station and increase with increased advertising on the other platform. If the probability that viewers of station j are informed of product i is αi+G(φji), then, the expected share of platform j's viewers who purchase product i is given by

The first term corresponds to the expected share if the consumer is informed only about product i, and the second term the expected share when the consumer is aware of both products.

Now they look at two types of equilibria; non-exclusive (NE) ones in which the platforms accept both advertisers, and exclusive equilibria, where the platforms offer exclusive contracts only to one advertiser. If both platforms take the same advertiser, then they call it an exclusive-same (ES) regime, and when each platform accepts a different advertiser, they call it an exclusive-different (ED) regime.

Assume that the marginal contribution of an advertiser from advertising is a positive decreasing function T(.). Then, comparing the outcomes in the three equilibria, we have the following conclusions:

1. The level of advertising: φED< φES = φNE

2. Prices: (pNE-c)<(pES-c)<(pED-c) where pES=average(p1ES, p2ES)

3. Payoff to the Station, C: For small α and large ts, CED>CES>CNE

For small ts and large α, CNE>CED and CNE>CES

The above results suggest that the marginal benefit obtained by the customer from the NE or the ES regime is higher than the ED regime. This is because by increasing advertising in the ED regime, one advertiser causes the platform to lose customers to the other platform, and therefore reduces its own reach. Since the advertiser advertises on both platforms in the NE and ES regime, it does not reduce its reach by increasing advertising.

From the above conclusion, the advertiser has the least incentive to advertise in the ED regime. The second conclusion is due to the differing levels of information that consumers have in the different regimes. Information available to consumers is highest in the NE regime, lowest in the ED regime and somewhere in between for the ES regime. For the platform, the choice of regime depends on the values of α and ts. For low values of α and/or high values of ts, advertising is the main source of information for the consumers, and so the platform can negotiate better even with lower levels of advertising, and so, the ED regime is most successful in deriving the best outcome for the platform, followed by the ES and then the NE regimes. The argument goes the other way for large values of α and low values of ts. Since stations are only a minor source of information between the buyer and the seller, they have a lower negotiation power and would prefer high advertising levels and attract smaller shares of both advertisers' advertising budgets.

Intra-Platform Competition with Bertrand Competition

The third paper described is the one by Armstrong (2006). Armstrong uses a simple model to argue that if firms can charge consumers for entry, then, platforms will allow competition within the platform. If they cannot charge for entry, they will restrict competition and try and increase the revenues they can extract from retailers.

Armstrong's model has two platforms with zero costs located at either end of the Hotelling line. He assumes that consumers can obtain a utility of ui1 from platform i and the share of the market is given by, ni1= ½+(ui1-uj1)/2t, where t is the transport cost (or the taste parameter).

There are retailers supplying a single homogenous good at a marginal cost, c. They set a price P, demand is given by q(P) and consumer surplus by v(P). The retailers are involved in a Bertand competition within the platform.

Armstrong considers two cases: one in which the platform can charge consumers for entry, and the second in which, entry charges are zero.

If the platform can charge for entry, then, the joint profits of the platform and the retailer is given by,

(½+(v(Pi)- pi1- uj1)/2t) (q(Pi)( Pi- C) + pi1)

where pi1 is the price consumers pay to access the platform, and the first term in parantheses is the size of the market, assuming that ui1= v(Pi)- pi1. Also, Armstrong assumes that the utility on one platform is independent of the nature of competition on the other platform. Profits are maximised when Pi=C and that the joint profit is entirely appropriated by the platform and the retailers earn zero profits. The equilibrium charge for access is p1=t.

Now, consider the second case where the platform cannot charge for entry. The platform can only obtain revenues from the retailer and the only way the retailer can earn positive profits is if it operates as a monopolist. This is clear from the joint profit (in this case, solely retailer profit) equation,

(½+(v(Pi)- pi1- uj1)/2t) (q(Pi)( Pi- C))

Also, depending on the value of t, the optimal price for the monopolist is chosen. If t is small, then, the optimal price is close to C and if t is large, it is closer to the monopoly price.

The model developed in this paper extends the Armstrong model to m retailers who engage in Cournot price competiton. The model is also extended to the Stahl case where the platform supplies a large number of products, i.e. the multi-product case and has conclusions that differ greatly from the single-product case.

## IV

## Intra-platform competition with Cournot Competition

A more extensive model of intra-platform competition is presented in this section. Consider a model with n-platforms. These platforms face two sides of demand. Following Armstrong's convention, call them retailers and consumers. The platform must now decide the optimal number of retailers, m, to court and the subscription charge, s, for the consumers. The platform charges a fee, F to each retailer. For simplicity, assume that the platform has zero costs. Therefore the platform must choose an (m,s) combination to maximise its profits, given by

ΠP = m (F + s q(m))

The number of consumers, q, is determined by the number of retailers on the platform, which determines the extent of competition and therefore the quantity sold on the platform. Let the retailers sell a homogenous commodity, and can multi-home. For simplicity, assume that each retailer on the platform faces the following profit function

Π= q(m) p S(p(m), s)

For simplicity, again, assume that the retailers have zero costs. Profits of the retailers are given by the quantity they manage to sell on the platform, multiplied by the price and the size of the customer base visiting the platform. The price, p, is determined by the following inverse demand equation, p=D(Q), where Q is the total output of the m-firms on the platform. The size, S, is a function of the price, p, charged on the platform and the subscription charge, s. These two functions determine the behaviour of the consumers. D is decreasing in Q and S is increasing in Q. Assume that the consumers single-home.

To arrive at an equilibrium, assume a Cournot-price competition between the m firms within the platform, and then with q(m), solve for the optimal (m,s) for the platform. Using the idea of backward induction, start with the retailer's decision, and then, use the retailer's optimal decision in the platform's problem.

## The Retailer's Problem

The retailer assumes (m,s) to be given, and decides on quantity.

The profit function re-written in terms of variables, is

Π= q(m) D(Q) S(Q)

The First Order Conditions with respect to q for the individual retailer is,

The first term is the direct gain in revenues from increasing quantity. The second term is the loss in profits due to a fall in prices. The last term is the gain in profits from other platforms. Now, to solve for q, we seek a symmetric equilibrium, where q = Q/m. Dividing throughout by D(Q) S(Q), using the symmetry condition and rearranging, we obtain the following condition,

Assume that elasticites of D and S with respect to Q are given by - eD Q(m+1) and eSQ(m+1) respectively. To support these, assume that D and S have the following functional forms.

D(Q)= exp( -eDQ(m+1)+c) and

S(Q,s)=exp(eSQ(m+1)-s)

where, c is the other factors that determine demand, that is exogenous demand, and s the subscription charged. The factor, c, will turn out to be a vital factor. One interpretation is that c represents the size of the demand from sources other than this particular market, i.e. the residual demand.

Substituting these in, we obtain,

Therefore, as the number of firms increases, the quantity sold within a platform increases.

Price and size are respectively given by,

Observe that as eD increases or eS falls, prices increase. So, as the opportunity to multi-home increases, eS falls, implying tougher competition between platforms and so, to retain consumers prices decline.

The profits of the individual retailer is given by,

## The Platform's problem

The platform then seeks to maximise its own profits, now that it knows how the retailer's profits and the quantity sold are determined by m and s.

In other words, it seeks to maximize its own profits over (m,s). To simplify the determination of F, assume that the firm can charge a fraction α of the retailer's profits as rent. Therefore the objective function of the platform is,

ΠP = m (α Π + s q(m))

Substituting the equations for Π and q(m),

First, consider the case where s>0. To get an idea of the optimal (m,s), plot the profit contours (with s on the vertical axis and m on the horizontal axis) for different values of c. Plot the profit curves for different values of c, These are shown as below. The lighter curves indicate higher profits.

c=0 c=1

c=5 c=10

Now, depending on the available options in m, i.e., the number of retailers willing to locate shop on the platform, the platform can decide on an optimal entry charge, and pick the m that maximises profits. The choice of m, as can be observed from the table and the figure, depends on the value of c. The firm can refer to a schedule estimating the different parameters and arrive at the optimal number of retailers to permit to maximize profits. There are a few points of interest that can be observed from the above figures.

Firstly, for large values of c, it is optimal to restrict competition and extract profits entirely from the retailer (i.e. set s=0).

Secondly, the platform is better off restricting competition for some values of c if the number of retailers willing to set up shop is bounded at some low level. For example, consider the case where c=5. If there are a limited number of retailers willing to locate on the platform, then, the platform is better off allowing only a monopoly.

## Changes in α

One restrictive assumption made was that the platform appropriates all the retailers' profits, i.e. α=1. Relaxing this changes the optimality results. Consider a specific example. A reduction α to 0.1 from 1 (for the c=5 case) changes the optimal from a monopoly-no subscription outcome to a large number of firms with positive subscription. For other values of c, the optimal remains unchanged for plausible ranges of m and s.

Therefore, another major factor in deciding the optimal competition within the platform is the share of the profits that the platform can extract as rents from the retailers. A more advanced model would make this share a function of the number of retailers and proceed through similar calculations.

α =0.1, c=5

## Subscription cannot be charged

If s=0, that is, if the platform cannot charge the consumers for entry, or it does not possess any other implicit source of revenue, then, the profit equation is

It can be seen that as for m≥1, m → ∞, ΠP → 0 and ΠP is decreasing in m. The function is plotted below (c=5, α =1 and eD-eS=1).

Therefore, if the platform cannot charge for entry, then, it should restrict competition to a monopoly. This agrees with the Armstrong model in its conclusion.

## Exogenous subscription

Consider the case where s is not the choice variable. As mentioned before, this is the case when the platform earns revenues indirectly from increased number of consumers, but cannot choose the 'entry charge', i.e. the case where s is exogenous.

The profit equation for the platform is the same as before.

This is similar to the previous problem, but for the fact that s is exogenous. The same figures and calculations hold true. For a given s, for low values of c, the platform is better off allowing more firms to enter. For higher values of c, the firm is better off restricting competition to a monopoly within the platform.

## Multiple product platforms

The conclusions above suggest that the platforms that have very high demand/markets should restrict competition to a single product. However, often we observe competition within the same platform, for example, at stores such as Harrod's and Selfridges, we observe competing brands of clothing being sold, and at malls, we see different music labels. The key assumption in the above was the fact that the platform sold only one product. An extension of the above model would be to relax this assumption to include multiple products to be sold on the same platform. Consider a platform that sells n different products, and has to decide on the number of firms mj for each product and a subscription/entry charge s.

The platform profits in this case, are the sum of profits in each market.

Profits in each product category are increasing in the number of firms in other products. Also, assume that the differences in elasticities in constant across products. These are rather restrictive assumptions, but, serve to illustrate the argument and to make the algebra simpler. We assume symmetry in the equilibrium m across the n products and the profit equation reduces to,

which is of the same form as the single product platform profits if n=1 and c=0. The contour plots are represented as below, with the lighter lines representing higher contours. The figure on the left is for the case when n=2, and the one on the right is for higher values of n, i.e. n>2. (c=5 in both cases; the plots do not differ qualitatively for other values of c)

From the figure below, it is clear that within a restrictive model, it is better to allow greater competition and to reduce subscription charges to a minimum, and to sustain a loss, on subscription (that is a non-positive s) if necessary.

## Multi-product platform without subscription

If subscription cannot be charged, then, the profit equation is

Plotting the profit function, with c=5 and n>2, we get the following curve

ΠP is decreasing in m, and so the platform should allow competition to maximize profits.

This extended model gives different conclusions from that of the single product platform with subscription charge. For similar values of c, different assumptions on the level of competition yield different optimality results.

Let us list out the conclusions developed in the above models

For low values of c, a single-product platform would choose a high subscription and the largest possible number of firms.

For high values of c, a single-product platform would choose a monopoly structure with close to zero subscription charges.

For all values of c, a multi-product platform would choose some amount of competition with zero subscription charges.

If the platform cannot charge subscription, then, it would choose a monopoly if it is a single-product platform and allow competition if it is a multi-product platform.

## V

## Applications

We now consider a few applications of the above models to specific industries.

## Low Exogenous demand:

The platforms in this model fix a level of subscription and try to maximise the number of firms on the other side of the market. Consider the case for operating systems, browsers etc. This case has a low exogenous demand. The major suppliers (Microsoft, Apple Corp and IBM) supply the user end software either at a high charge (the vertical section of the profit coutour in the c=0 or 1 case in the single product platform case) or as free ware (horizontal section of the profit contours) and try to increase the number of software developers.

## Large Exogenous demand

## Multi-product case:

According to this model, there are a variety of products available on each platform supplied by competing firms, and the platform charges a zero or negative subscription charge to consumers.

Consider the case of shopping centres. This category of platforms includes supermarkets, shopping malls, shopping centres at transport junctions (airports, bus stations etc), multi-brand stores etc. These malls have a large number of products sold by non-monopoly retailers and they do not charge entry or subscription charges, as predicted by the multi-store model.

## Single-product case:

## Implicit advertising:

This includes unobtrusive advertising during major events such as the Olympics, the FIFA World Cup etc, or advertising within movies, TV series etc. where advertising does not hinder from consumer's utility from the platform (unless the consumer is strongly put off by any form of branding). Since there is no disutility from greater advertising, this case can be modelled with the model. The optimal outcome for the producers is to charge the advertisers and charge very low subscription amounts (at least, less than optimal) to viewers.

## Obtrusive Advertising:

Advertising with subscription charges: Most media treat advertisers as profit centres and have zero or negative subscription charges. Examples of these platforms are TV, Radio, newspapers, social networking sites, email service providers and other internet portals. Since, in these models, consumers do not derive utility from advertising directly, and because more advertising has significant negative influence on utility (as opposed to more output, and therefore, lower prices), the model outlined in the previous section does not fit this case. The Dukes and Gal-Or model is a more suitable model as it incorporates advertising utility directly.

## VI

## Conclusion

The models presented give a more complete picture of competition within platforms, and fit observations better. Depending on the size of exogenous demand, the level of bargaining, the variety of retailers, the platform would choose to allow differing levels of competition. Extensions to this model would be to incorporate the bargaining game between the retailers and the platform, which would endogenize α. Other points of departure could be along the lines of a more general demand function, or product differentiation between the platforms, along the lines of the circular city model. Notwithstanding these relaxations and other strict assumptions about costs and the structure of the game, these models are a better description of reality and are richer in detail.