Two-sided markets: a progress report.

We provide a road map to the burgeoning literature on two-sided markets and present new results. We identify two-sided markets with markets in which the structure, and not only the level of prices charged by platforms, matters. The failure of the Coase theorem is necessary but not sufficient for two-sidedness. We build a model integrating usage and membership externalities that unifies two hitherto disparate strands of the literature emphasizing either form of externality, and obtain new results on the mix of membership and usage charges when price setting or bargaining determine payments between end-users.

1. Introduction

[] Two-sided (or, more generally, multi-sided (1)) markets are roughly defined as markets in which one or several platforms enable interactions between end-users and try to get the two (or multiple) sides "on board" by appropriately charging each side. That is, platforms court each side while attempting to make, or at least not lose, money overall.

Examples of two-sided markets readily come to mind. Videogame platforms, such as Atari, Nintendo, Sega, Sony Play Station, and Microsoft X-Box, need to attract gamers in order to persuade game developers to design or port games to their platform, and they need games to induce gamers to buy and use their videogame console. Software producers court both users and application developers, client and server sides, or readers and writers. Portals, TV networks, and newspapers compete for advertisers as well as "eyeballs" And payment card systems need to attract both merchants and cardholders. There are many other two-sided markets of interest (2) only a few of which will be mentioned in this article.

But what is a two-sided market, and why does two-sidedness matter? On the former question, the recent literature has been mostly industry specific and has had much of a "You know a two-sided market when you see it" flavor. "Getting the two sides on board" is a useful characterization, but it is not restrictive enough. Indeed, if the analysis just stopped there, pretty much any market would be two-sided, since buyers and sellers need to be brought together for markets to exist and gains from trade to be realized. We define a two-sided market as one in which the volume of transactions between end-users depends on the structure and not only on the overall level of the fees charged by the platform. A platform's usage or variable charges impact the two sides' willingness to trade once on the platform and, thereby, their net surpluses from potential interactions; the platforms' membership or fixed charges in turn condition the end-users' presence on the platform. The platforms' fine design of the structure of variable and fixed charges is relevant only if the two sides do not negotiate away the corresponding usage and membership externalities.

Conceptually, the theory of two-sided markets is related to the theories of network externalities and of (market or regulated) multi-product pricing. From the former, initiated by Katz and Shapiro (1985, 1986) and Farrell and Saloner (1985, 1986), (3) it borrows the notion that there are noninternalized externalities among end-users. (4) From the latter, it borrows the focus on price structure and the idea that price structures are less likely to be distorted by market power than price levels. The multi-product pricing literature, however, does not allow for externalities in the consumption of different products: to use a celebrated example, the buyer of a razor internalizes in his purchase decision the net surplus that he will derive from buying razor blades. The starting point for the theory of two-sided markets, by contrast, is that an end-user does not internalize the welfare impact of his use of the platform on other end-users.

The rest of the article is organized as follows. In Section 2, we introduce platforms and end-users as well as the general setting. Section 3 focuses on pure usage charges and provides conditions for the allocation of the total usage charge (e.g., the price of a call or of a payment card transaction) between the two sides not to be neutral; the failure of the Coase theorem is necessary but not sufficient for two-sidedness. We analyze pure membership externalities in Section 4.

Section 5 builds a canonical model of two-sided markets and applies it to pure-usage and pure-membership externalities. This model allows us to unify and compare the results obtained in the two hitherto disparate strands of the literature emphasizing either form of externality. Section 5 then shows that in the presence of (price-setting or bargaining-based) payments among end-users, the pure-membership-externalities model applies under some conditions, and it derives general results for the setting of usage charges. Finally, the section discusses several relevant extensions of the canonical model.

Section 6 summarizes our main conclusions. Needless to say, our overview is somewhat selective in its choice of topics and articles. We highly recommend the excellent and complementary coverages in Armstrong (2006) and Jullien (2005).

2. Membership and usage externalities

[] Suppose that there are potential gains from trade in an "interaction" between two end-users, whom for convenience we will call the buyer (B) and the seller (S). A platform enables or facilitates the interaction between the two sides provided that they indeed want to interact. (5) The interaction can be pretty much anything, but it must be identified clearly. In the case of videogames, an interaction occurs when a buyer (garner) buys a game developed by a seller (game publisher) and plays it using the console designed by the platform. Similarly, for an operating system (OS), an interaction occurs when the buyer (user) buys an application built by the seller (developer) on the platform. In the case of payment cards, an interaction occurs when a buyer (cardholder) uses his card to settle a transaction with a seller (merchant). The interaction between a "viewer" and an advertiser mediated by a newspaper or a TV channel occurs when the viewer reads the ad. The interaction between a caller and a receiver in a telecom network is a phone conversation, and that between a website and a web user on the Internet is a data transfer.

We distinguish between membership charges and usage charges, and between membership externalities and usage externalities. Gains from trade between end-users almost always arise from usage: (6) the cardholder and the merchant derive convenience benefits when the former uses a card rather than cash; a caller and a callee benefit from their communication, not per se from having a phone; and so forth. Usage decisions depend on how much the platform charges for usage. As depicted in Figure 1, the platform charges a price or access charge [a.sup.S] to the seller and [a.sup.B] to the buyer for enabling the interaction. For example, American Express charges a merchant discount to the merchant, so [a.sup.S] > 0, while the buyer pays nothing for using the American Express card, [a.sup.B] = 0. (7) Similarly, a caller is charged a per-minute calling charge and the receiver a per-minute reception charge. Usage externalities arise from usage decisions: if I strictly benefit from using my card rather than cash, then the merchant exerts a (positive) usage externality on me by accepting the card. Similarly, if I benefit from being able to call a friend on his mobile phone, then this friend's willingness to give me his number and receive the call exerts a positive usage externality on me.

[FIGURE 1 OMITTED]

Ex ante, the platform may charge interaction-independent fixed fees [A.sup.S] and [A.sup.B]. For example, American Express charges yearly fees to cardholders ([A.sup.B] > 0). In the case of videogames, platforms may charge fees to game developers for development kits ([A.sup.B] > 0) on top of royalties per copy sold ([a.sup.S] > 0); they charge gamers for the videogame console ([A.sup.B] > 0). For Windows, Microsoft charges a usage-independent fee to consumers ([A.sup.B] > 0) but no variable fees ([a.sup.S] = [a.sup.B] = 0). To the extent that an end-user on side i derives a strictly positive net surplus from interacting with additional end-users on side j [not equal to] i, membership decisions generate membership externalities.

3. Pure usage externalities

[] Let us first focus on the elementary situation in which membership is given. While restrictive, this situation already encompasses a number of industries of interest, for example a mature telecommunications market in which everyone has a phone or a mature payment system in which no substantial fixed cost or charge stands in the way of membership. Furthermore, and as Section 5 will show, the pure-usage-externalities paradigm is relevant even for some industries with endogenous memberships.

The interesting question is then whether end-users intensively use the platform rather than whether they join it. We therefore introduce a distinction between the price level, defined as the total price charged by the platform to the two sides, and the price structure, referring to the decomposition or allocation of the total price between the buyer and the seller.

[] Defining two-sidedness.

Definition 1. Consider a platform charging per-interaction charges [a.sup.B] and [a.sup.S] to the buyer and seller sides. The market for interactions between the two sides is one-sided if the volume V of transactions realized on the platform depends only on the aggregate price level

a = [a.sup.B] + [a.sup.S],