Group for Research in Decision Analysis

# Time-Consistent Equilibria and Differential Games with Time Inconsistent Preferences

## Jesús Marín Solano – Universitat de Barcelona, Spain

Time-inconsistent preferences are introduced in intertemporal decision problems. 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 addressed. The results are illustrated with two examples: a common property resource game and a linear state pollution differential game.