Time-Consistent Equilibria in a Differential Game Model with Time Inconsistent Preferences and Partial Cooperation

Differential games with time-inconsistent preferences are studied. Noncooperative Markovian Nash equilibria are described. If players can cooperate at every instant of time, time-consistent equilibria are analyzed for the problem with partial cooperation. Cooperation is partial in the sense that, although players cooperate at every moment t forming a coalition, due to the time inconsistency of the time preferences, coalitions at different times value the future in a different way, and they are treated as different agents. Time-consistent equilibria are obtained by looking for the Markovian subgame perfect equilibria in the corresponding noncooperative sequential game. The issue of dynamic consistency is then considered. In order to guarantee the sustainability of cooperation, players should bargain at every instant of time their weight in the whole coalition, and nonconstant weights are introduced. The results are illustrated with two examples: a common property resource game and a linear state pollution differential game.

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