Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility

In this paper, we study the time consistency of cooperative agreements in dynamic games with non-transferable utility. An agreement designed at the outset of a game is time-consistent (or sustainable) if it remains in place for the entire duration of the game, that is, if the players would not benefit from switching to their non-cooperative strategies. The literature has highlighted that, since side payments are not allowed, the design of such an agreement is very challenging. To address this issue, we introduce different notions for the temporal stability of an agreement and determine endogenously the duration of the agreement. We illustrate our general results with a linear-quadratic difference game and show that an agreement’s duration can be easily assessed using the problem data. We also study the effect of information structure on the endogenous duration of the agreement. We illustrate our results with a numerical example.