Nonzero-Sum Markov Games with Finite Random Horizon

This manuscript aims to establish the existence of a Nash equilibrium in nonzero-sum Markov games with a random horizon of finite support. The proof relies on dynamic programming techniques adapted to the stochastic nature of the horizon and the interaction between players. Introducing a random horizon with finite support allows for a more realistic modeling of scenarios in which the duration of the game is uncertain and influenced by exogenous random events. To illustrate the applicability of the theoretical results, we examine a dynamic game version of the Great Fish War, which models competition over a renewable resource under uncertainty about the duration of exploitation. This framework enhances the applicability of Markov game theory to decision-making contexts where time horizons are unpredictable.