Dynamic Coalitional Agreements - coalitional rationalizability in multi-stage games

This paper extends the concept of coalitional rationalizability of Ambrus(01) to incorporate sequential rationality in multi-stage games with observable actions and incomplete information. Agreements among players are implicit, it is assumed that players cannot communicate with each other during the game. They re°ect a reasoning procedure which entails restricting strategies in a mutually advantegous way. They can be conditional on observed histories and players' types, which corresponds to allowing players to make agreements ex post and along the course of play. An agreement that is conditioned on a history is evaluated from the point of view of that history. This introduces a dynamic interaction among coalitional agreements with features of both backward and forward induction. Coalitional agreements iteratively de ̄ne the set of extensive form coalitionally rationalizable strategies. This solution concept has a number of analogous properties with normal form coalitionally rationalizability. It is always nonempty. The set of outcomes consistent with it is a subset of the outcomes consistent with extensive form rationalizability, and it is robust to the order in which agreements are made. In games of perfect information extensive form coalitional rationalizability is outcome equivalent to extensive form rationalizability. Perfect coalition-proof Nash equilibria and renegotiation-proof Nash equilibria do not have to be contained in the solution set, even in two-player games, because those concepts do not imply forward induction reasoning. An alternative notion of extensive form coalitional rationalizability is also provided, assuming that coalitional agreements can only be made ex ante, but sequential individual rationality is maintained. * Princeton University and Yale University. I thank Stephen Morris, David Pearce and especially Dilip Abreu for useful comments and suggestions. I also bene ̄tted from conversations on the topic with Faruk Gul, Wolfgang Pesendorfer and Marciano Siniscalchi. I am grateful to the Cowles Foundation for the fellowship they granted me when I was working on this paper.