Non-Cooperative Representations of Cooperative Games

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although these games study distinct aspects of social behavior, this paper proposes a novel attempt at relating the two models. In particular, cooperative games may be represented by a non-cooperative game in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When these coalitions play against one another, the equilibrium payoffs for each coalition coincide with what is predicted by the worth function. This paper proves sufficient conditions under which cooperative games can be represented by non-cooperative games. This paper finds that all strictly superadditive partition function form (PFF) games can be represented under Nash equilibrium (NE) and rationalizability; that all weakly superadditive characteristic function form (CFF) games can be represented under NE; and that all weakly superadditive PFF games can be represented under trembling hand perfect equilibrium (THPE).