SFB 303 Discussion Paper No. B - 144
Author: Selten, Reinhard, and Myrna H. Wooders
Title: A Game Equilibrium Model of Thin Markets
Abstract: 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.
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Creation-Date: April 1990
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