Buyers have several means of payments available: cash, debit cards, credit cards. Merchants are obliged to accept cash, but can choose to accept other media. Most banks offer simultaneously debit and credit cards to both, the latter often with some incentives. Wonder why?
Wilko Bolt and Sujit Chakravorti show that banks are the big winners while both merchants and consumers are losers. The reason is that banks can rig the payment fees in such a way to force merchants to accept credit cards that bear higher fees. The key here is that merchants are not allowed to differentiate prices by type of payment medium.
The analysis is performed with an elaborate model where all three players make endogenous decisions on what to accept, offer or use, and takes into account the consumer's worry about theft the timing mismatch of income and expense, the merchant's worry about getting sales and the banks worry about bad credit. This allows to be more explicit about the welfare gains (or losses of each agent). Unfortunately though, risk neutrality is assumed for consumers. Risk aversion will make them willing to pay even higher card fees, leading even further away from a social optimum. So it looks like some strong regulation is needed here. Or allow merchants to charge different prices by type of payment.