Renegotiation in the Repeated Cournot Model
by
M. Aramendia
Universidad del Pais Vasco
Coauthors: C. Larrea, L. Ruiz

With the aim of avoiding subgame perfect equilibriums which are likely to be renegotiated different concepts of renegotiation-proofness have been introduced. However, the definitions given by the authors are quite different and in some cases lead to opposite results. We concentrate on the two best-known concepts of renegotiation: the Consistent Bargaining Equilibrium (CBE) of Abreu, Pierce and Stachetti and the (Weak) Renegotiation Proof Equilibrium (WRP) of Farrell and Maskin. We compare these two concepts in a specific but natural problem: the perfect monitoring Cournot supergame with several players. It is well known that, in this model, the symmetric monopoly outcome can be sustained as a subgame perfect equilibrium for any finite number of players provided that they are sufficiently patient. We find this result unsatisfactory since when the number of players tends to infinity the situation must tend to perfect competition. So a natural question arises: Is it still possible to sustain the monopoly outcome as a renegotiation proof equilibrium when the number of players is big enough? We first see that the answer to this question is basically affirmative with both the CBE and WRP concepts. We also show that the WRP concept may lead to rather asymmetric payoffs during the punishment path of any player. This seems unreasonable since all the players are equal. At the other extreme, the CBE concept leads, in our model, to strongly symmetric strategy profiles, which means that all the players have to produce exactly the same in all periods, even after the deviation of a player. As a consequence all the players suffer equally the punishment of the cheater. Neither do we find reasonable the claim of the cheater for same payoffs in the continuation of the game since when a player cheats he obtains much more benefits than the others. Then we introduce a new definition of renegotiation proofness. It is suitable for symmetric games and it is closer to that of Farrell and Maskin with an additional restriction. The WRP concept requires that, in equilibrium, no continuation payoff be Pareto dominated by another continuation payoff. In addition we ask for a kind of reasonable symmetry to exclude those equilibria in which planned punishments hurt any of the punishers. We will call this concept Partially Symmetric Weak Renegotiation Proof equilibrium (PSWRP). This concept significantly limits the cooperative outcomes that can be sustained. In particular, when the number of players tends to infinity (even for a discount factor arbitrarily close to 1), i) the collusive benefits that could be sustained as a PSWRP equilibrium are, at most, four times the Cournot benefits; ii) the reasonable collusive price that can be sustained in equilibrium tends to the Cournot price. We write reasonable price because technically it is possible to sustain a price significantly higher than the Cournot price, but this is not reasonable in a sense to be specified. All the results holds in the Cournot model with the standard assumptions.

Date received: June 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafk-38.