A Game Equilibrium Model of Thin Markets

We consider games of group, or coalition, formation occuring over infinite, discrete time, with new participants becoming active in the game in each period, and with participants that have successfully formed groups leaving the game each period. Markets may be “thin”, in the sense that the number of participants active in the game in any time period is finite and may be small. We construct a subgame perfect equilibrium for an example and show some additional properties of the equilibrium. One property is that, even though markets are thin, the “first mover” within a time period has an advantage (and realizes more than a competitive payoff) only in special circumstances, and, along the equilibrium path, he is the only mover who can have such an advantage. Also, we discuss the limit behavior of the model as costs of waiting (time costs) become small; specifically, the equilibrium payoffs converge to core payoffs of a game with a continuum of players and finite coalitions (f-core payoffs). The static continuum game provides an idealization of the limit of the dynamic games for small waiting costs. Thus our research initiates providing a noncooperative foundation for the core as a solution concept for such games.