ABSTRACT
In the following paper we will report on the development and empirical application of a model for the equilibrium behavior of three-person interaction systems. The context in which the members of the system interact is a laboratory situation known as the coalition game. The simplest description of a three-person coalition game is that it is an experimental game in which on each of a series of trials players attempt to form an alliance, and if successful, those participating in the alliance receive a payoff. The usual rule governing the formation of alliances is that only two of the players may enter into a coalition on any trial. The game may therefore be described as a mixed-motive game, since there are elements of competition in that no outcome satisfies everyone, and there are elements of cooperation in that two players must ally in order to win. What we mean by the equilibrium behavior of such an interaction system is the set of stable, probabilistically described strategies used by players in the game. We will propose and then demonstrate that such interaction systems stabilize over time and that the point at which they stabilize is that point which maximizes the expected utility of the participants in the interaction.
