Robust Stable Payoff Distribution in Stochastic Cooperative Games

Cooperative games with transferable utilities belong to a branch of game theory where groups of players can enter into binding agreements and form coalitions in order to jointly achieve some objectives. In a cooperative setting, one of the most important questions to address is how to establish a payoff distribution among the players in such a way to ensure the stability of the game. Classical solution concepts such as the core and the least core are only defined in games with deterministic characteristic functions. However, the payoff function might not be exact due to estimation/approximation errors, and classical solution concepts are no longer applicable. We redefine the concept of stability in a stochastic setting and introduce new concepts for robust payoff distribution. We demonstrate these concepts with a number of games including the stochastic newsvendor games. Properties and numerical schemes for finding the robust solutions are presented.