Sequentially Stable Coalition Structures

Abstract

In this paper, we examine the question of which coalition structures are formed in cooperative games with externalities. We introduce a stability concept for a coalition structure called a sequentially stable coalition structure by extending the concept of an equilibrium binding agreement (EBA) due to Ray and Vohra (1997). In an EBA, coalitions can only break up into smaller sizes of coalitions, but not merge into larger sizes of coalitions. On the other hand, in our concept of sequential stability, both breaking up and merging are allowed for coalitions. We also use a “step-by-step” approach to describe negotiation steps concretely by restricting how coalition structures can change: when one coalition structure is changed to another one, either (i) only one merging of two separate coalitions into a coalition occurs, or (ii) only one breaking up of a coalition into two separate coalitions happens. As an application of our stability notion, we show that the coalition structure consisting of only the grand coalition structure can be sequentially stable in common pool resource games.