When Do Coalitions Survive Over Time? Stationary Stability in Dynamic Cooperative Games

Abstract

This paper develops a framework based on dynamic hedonic games, a special class of cooperative games, to find conditions for the temporal stability of coalitions for situations where the values of coalitions for players are allowed to change depending on the history of play. We define two notions of dynamic stability and provide conditions that guarantee that a dynamic hedonic game has a stationary stable outcome as well as conditions that guarantee that all dynamically stable outcomes of a game are stationary. We show through a number of examples that all these conditions are needed to guarantee the existence of dynamically stable stationary outcomes and rule out the existence of non-stationary dynamically stable outcomes. In the end, we apply our results to an extended example of people's decisions regarding interactions in smaller social groups during a pandemic.

Keywords: C71, D20, D7