RDP 2009-02: Competition Between Payment Systems 1. Introduction

Over the past decade, analysis of the pricing strategies of payment system operators has been an area of growing interest. Much of this analysis has, however, been conducted in the context of a single payments platform, competing with the default alternative of cash. Only recently has a literature developed examining the more complex, but more realistic, situation of competing payment systems.

Important contributions in this latter area include Rochet and Tirole (2005), Armstrong (2006) and Guthrie and Wright (2007). In these and other papers, considerable progress has been made in identifying key issues influencing platform pricing. However, the complexity of modelling competition between payment systems has typically required such papers to adopt a range of simplifying assumptions, some of which limit the applicability of any findings.

One such assumption is that payment platforms levy purely per-transaction fees on both consumers and merchants. Adopting this assumption has the analytical advantage of ensuring that every consumer (merchant) faces the same charge for each transaction on a given platform as every other consumer (merchant). However, in many payments markets competing schemes tend to use annual, rather than per-transaction, fees in their pricing to consumers.^[1] In such markets, the effective per-transaction fee faced by consumers, rather than being identical for all consumers, varies depending on their propensity to use a given network.

A second assumption commonly adopted relates to the degree to which consumers (merchants) tend to hold (accept) multiple payment instruments – known as multi-homing. In recent years the relative tendency of consumers and merchants to multi-home has emerged as an important potential determinant of platforms' allocation of their fees between the two groups. However, allowing for multi-homing on both sides of payments markets significantly complicates analysis of aggregate consumer and merchant behaviour, and hence of platforms' pricing incentives. It has therefore been common – an example is Chakravorti and Roson (2006), discussed in greater detail below – to assume that multi-homing is allowed only on one side of the market, with participants on the other side permitted to subscribe to at most one platform (single-home).

Finally, three further simplifying assumptions often adopted are: that competing platforms provide identical bundles of payment services to both consumers and merchants; that they face identical costs in providing these services; and that consumers or merchants are homogeneous in the values that they place on the benefits they receive from transacting with each platform. These assumptions considerably ease the task of understanding the mechanics of competition between platforms. They also allow consumers or merchants to be treated as identical in the transactional benefits they receive not only across platforms but across individuals. This dramatically (albeit unrealistically) simplifies modelling of the balancing task each platform faces in trying to get ‘both sides on board’, so as to maximise profit. These assumptions do, however, limit the scope for such analysis to inform our understanding of competition between, say, different types of payment instruments, such as debit versus credit cards.

Against this background, the central goal of this paper is to construct a model of competition between payment systems which relaxes as many as possible of these assumptions. We would also like the model to be implementable, so as to allow the use of simulation analysis to study the pricing implications of such competition.

Much of the literature to date on such competition has tended to be purely analytical – focusing, for example, on deriving the marginal conditions that will be satisfied at a profit-maximising equilibrium (in terms of suitably defined elasticities of consumer and merchant demand) and how these conditions will be affected by underlying features of the two sides of the market. Such analysis is both illuminating and important. However, it can also be valuable at times to be able to study the full solution to a model of any system. Such global solutions – in the current setting comprising each platform's ultimate pricing choices, their profits, and the final take-up of each platform's services by both consumers and merchants – can help not only to draw out interesting features of the system being modelled, but also illustrate how these features may respond as underlying parameters of the system are varied.

With these goals in mind, the model we develop is an extension of Chakravorti and Roson (2006). Their paper considers the case of two payment platforms competing with each other, along with the default payment option of cash.

A desirable feature of the Chakravorti and Roson (CR) model is that each platform, while charging merchants on a per-transaction basis, levies a fixed fee on consumers for joining the platform. Their model thus avoids the first (and arguably most restrictive) of the common limiting assumptions described above. It also explicitly allows for: heterogeneity among both consumers and merchants in the values they place on the transactional benefits provided by each platform; and, in principle at least, variation between the platforms in both the payment services they provide and the costs they incur in doing so.^[2]

Finally, an additional strength of the CR model is that it incorporates the ‘derived demand’ aspect of payments that many generic models of two-sided markets fail to capture. This is the property that payment transactions occur only as a by-product of the desire to undertake some other transaction – namely the exchange of a good or service – rather than being supplied or demanded for their own sake. All of these features contribute to making Chakravorti and Roson's framework a good starting point for modelling competition between payment systems.^[3]

The CR model does, however, assume that while merchants may choose to accept payments from neither, one or both platforms, consumers may at most subscribe to one platform. It thus incorporates the second of the common limiting assumptions listed earlier. The key extension we make is to remove this restriction on consumers, so as to be able to study the implications of fully endogenous multi-homing on both sides of the market for the pricing strategies of competing payment platforms. This turns out to have substantial ramifications for the behaviour of both consumers and merchants, and hence for platforms' pricing strategies towards each group.

The remainder of this paper is devoted to describing our extension of the CR model – henceforth referred to as our ECR model (for ‘Extended Chakravorti and Roson’) – and exploring its implications, in theoretical terms, for the behaviour of consumers, merchants and platforms. Section 2 of the paper sets out the details of our ECR model, as well as introducing essential notation. It also discusses possible applications of the model, including to competition between different types of payment instruments. Section 3 then focuses on establishing geometric frameworks for understanding the aggregate decisions of consumers to hold and merchants to accept the competing payment instruments in the model, and how these will be influenced by the pricing choices of the platforms.

In Section 4 we analyse an interesting new potential source of non-uniqueness in the behaviour of consumers and merchants in our model, and explore its possible implications for the ‘chicken and egg’ debate in relation to payment systems (and two-sided markets more generally). Numerical simulation of the model is deferred to the sequel to this paper, where (inter alia) the results of such simulations are used to further investigate the likely effects of competition on platforms' pricing strategies.^[4] Conclusions are drawn in Section 5.

Footnotes

An example is the credit card market in Australia. Of course many credit cardholders in Australia also receive reward points per dollar spent – equivalent to a negative per-transaction charge. However, they must usually pay an additional annual fee for membership of a rewards program. [1]

In practice, however, it should be noted that for the CR model the analysis of competition in the case of ‘non-symmetric’ platforms is ‘very complex, and general analytical results cannot be readily obtained’ (Chakravorti and Roson 2006, p 135). This practical limitation carries over to the model we develop in this paper. [2]

The CR model does not, however, allow for ‘business stealing’ considerations. This is the phenomenon – analogous to the well-known ‘prisoner's dilemma’ – whereby each individual merchant may feel compelled to accept payments from a platform, even if they would prefer (say) to be paid in cash, for fear that if they do not then some consumers who wish to use that platform might transfer their business to a competitor. In developing our extension of the CR model we also do not attempt to allow for business stealing considerations. This is not because we regard them as unimportant, but simply because analysis of them is not a particular goal of this paper – and omitting them simplifies the model, without obscuring those aspects of payments system competition which we do wish to investigate. [3]

See Gardner and Stone (2009a). After developing our ECR model we became aware that a somewhat similar study of the impact of allowing endogenous multi-homing on both sides of the market had already been undertaken in Roson (2005). Indeed, that paper allows, in principle, for additional features which our ECR model does not, such as multi-part (flat and per-transaction) pricing by platforms to both sides of the market, as well as both multi-part costs to platforms and multi-part benefits to consumers and merchants. However, it does not develop the geometric frameworks for understanding consumers' and merchants' card choices developed here, nor does it appear to explicitly address the non-uniqueness issues, canvassed in Section 4 of this paper, which can arise in such a model. Our own simulation analysis also suggests that there may be ‘starting-point dependency’ issues associated with the iterative approach used there – as described in Footnote 8 of Roson (2005, p 14) – to generate numerical simulation results. [4]