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

Abstract

Why do coalitions of people or firms stay intact overtime in some situations, while in other situations the size and members of the coalitions change frequently? 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. We show through a number of examples that all these conditions are needed to guarantee stable stationary 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: Cooperative Games, Dynamic Hedonic Games, Coalition Formation, Dynamic Stability, Pandemic,

JEL Classification: C71, C73, D00, D710