We consider the class of stochastic games played over finite event trees, that is, games where the random process is an act of nature and is not influenced by the players' actions. We suppose that the players agree to form the grand coalition and maximize their joint payoff. If the cooperative solution is not an equilibrium, then players may cheat on the agreement, unless a mechanism is designed to ensure that all players implement their cooperative controls over time (and nodes). To sustain cooperation over the event tree, we use behavior strategies known as grim trigger strategies. As we are dealing with a finite horizon, it is well known that deviation from cooperation in the last stage cannot be deterred, as there is no possibility for punishing the deviator(s). Consequently, we focus on epsilon (or approximated) equilibria. More specifically, we prove the existence of an epsilon-perfect equilibrium, where the value of epsilon is calculated using the game's parameters. We illustrate our findings with a numerical example.
Published May 2015 , 16 pages