Costly Renegotiation in Repeated Bertrand Games

This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of McCutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion.