RDP 2009-03: Competition Between Payment Systems: Results 1. Introduction

A common finding in the literature on competition between payment systems has been that an increase in the relative propensity of either consumers or merchants to single-home – that is, to hold or accept only a single payment instrument (besides cash) – will lead payment networks to price more attractively to that side of the market.[1] The results we present in this paper challenge the universal applicability of this finding.

These results are obtained from numerical simulations of a model of payment system competition developed in Gardner and Stone (2009a). The contrary finding we obtain from this model stems from the fact that it avoids two key simplifying assumptions commonly made in the literature.

The first such assumption is that one side of the market may subscribe to at most one payment network – that is, must single-home. We impose no such restriction, so that consumer and merchant decisions are fully endogenous. Second, it is also commonly assumed that networks charge both consumers and merchants on a purely per-transaction basis. By contrast, in our framework consumers face a flat subscription fee for joining a network rather than per-transaction fees – which better matches the reality of (say) card payment markets, where cardholders are typically charged an annual fee.

Several existing models incorporate one or other of these modifications. However, relaxing both assumptions simultaneously creates a fundamental change, by allowing the effective price consumers pay for each transaction to vary across individuals depending on how intensively they use each payment instrument. We demonstrate that having different consumers face different effective per-transaction prices for the same instrument has important consequences for both consumer and payment network behaviour. In particular, it breaks the positive nexus, previously found in the literature, between consumers' propensity to single-home and the attractiveness of the pricing they will be offered by competing platforms.[2]

We obtain our findings by comparing results from three main models: the framework developed in Chakravorti and Roson (2006), referred to here as the ‘CR’ model; our extension of this, set out in Gardner and Stone (2009a), which we refer to as our ‘ECR’ or ‘Extended Chakravorti and Roson’ model; and a third model developed in Section 4 of this paper. This latter model, which we refer to as our ‘Per-transaction Pricing’ or ‘PTP’ model, is identical to our ECR model in all respects except with per-transaction pricing rather than flat fees to consumers. A brief recap of the CR and ECR models is provided in Section 2. Section 3 presents simulation results for these two models, from which our main finding emerges. Section 4 then develops the PTP model and uses it to concretely confirm the key role of flat rather than per-transaction pricing in generating our contrary findings.

This paper also contains a second main set of findings. These concern how the assumption regarding which side of the market holds the choice of payment instrument at the moment of sale (typically taken to be consumers) affects competing platforms' relative pricing to merchants and consumers. For simplicity, we investigate this issue in the context of purely per-transaction pricing to both sides of the market, using our PTP model.

Clearly, once platforms have set their fees and all card holding and acceptance decisions have been made, holding the choice of payment instrument confers a benefit on consumers relative to merchants at the moment of sale. However, in terms of the pricing they will be offered by competing platforms ex ante, it is less clear whether having this choice would be expected to prove a blessing or a curse to consumers as a group.

Hermalin and Katz (2006) first noted that consumer choice at the moment of sale might lead to a phenomenon whereby competing platforms bias their pricing in favour of merchants rather than consumers. In a simple model, platforms would behave this way to minimise the impact on their profits from merchants seeking to alter consumers' payment choices via ‘steering’.[3]

Our own results confirm this phenomenon, and also Hermalin and Katz's observation that, in a modelling framework with purely per-transaction pricing, the extent of the bias against the side with the choice of instrument declines as the per-transaction cost to platforms of processing payments increases. Further, we show that the strength of this bias also decreases: first, as platforms' per-subscriber costs of signing up new cardholders rise; and second, as consumers exhibit a greater innate propensity to single-home.[4] All of these results are presented in Section 5, while Section 6 concludes.


For example, Rochet and Tirole (2003) list as one of six key insights that ‘an increase in multihoming on the buyer [consumer] side facilitates steering on the seller [merchant] side and results in a price structure more favorable to sellers’ (p 1013). Similarly, Guthrie and Wright (2003) note that ‘when consumers hold only one card, the effect of competition between card schemes is to make it more attractive for each card scheme to lower card fees to attract exclusive cardholders to their network’ (p 16). [1]

Our results also show that, even when platforms do use purely per-transaction pricing, an increasing propensity to single-home on one side leads to that side receiving more attractive relative pricing only if it also holds the final choice of instrument at the moment of sale. [2]

We use the term ‘steering’ here in the formal sense of the refusal by a merchant to accept a platform's cards, so as to force consumers who multi-home to use the card of a rival platform preferred by the merchant. [3]

In the latter case this is consistent with the intuition that while platforms face competitive pressure to forestall ‘steering’ by whichever side does not hold the choice of instrument (by pricing attractively to that side), this pressure should diminish as consumers' tendency to carry the cards of multiple platforms falls. [4]