Subgame Consistency Under Asynchronous Players’ Horizons

Abstract

In many game situations, the players’ time horizons differ. This may arise from different life spans, different entry and exit times, and the different duration for leases and contracts. Asynchronous horizon game situations occur frequently in economic and social activities. In this Chapter, subgame consistent cooperative solutions are derived for differential games with asynchronous players’ horizons and uncertain types of future players. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are derived. This analysis extends the application of cooperative differential game theory to problems where the players’ game horizons are asynchronous and the types of future players are uncertain. In particular, the Chapter is an integrated disquisition of the analysis in Yeung (2011) with an extension to incorporate stochastic state dynamics.