Platform Competition With User Rebates Under No Surcharge Rules

We analyze competing strategic platforms setting fees to a local monopolist merchant and granting cash-back rebates to end users, when the merchant is prevented from surcharging platforms customers, as frequently occurs with credit cards. Each platform has an incentive to gain transactions by increasing the spread between its merchant fee and user rebate above its rival's spread. This incentive yields non-existence of pure strategy equilibrium in many natural environments. In some circumstances, there is a mixed strategy equilibrium where platforms choose fee structures that induce the merchant to accept only one platform with equal probability, a form of monopolistic market allocation