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A Theory of Coalition Formation in Constant Sum Games

A finite set of agents N , endowed with heterogeneous abilities, compete for a share of the reward K. Agents receive a reward share determined by their individual abilities: higher is the agent’s relative position in N , in terms of ability, greater is the agent’s share. If agents form coalitions, the cooperation increases the abilities of all members, over their endowed ability. Thus, forming a coalition is mutually beneficial to all its members, although they are competitors. Such coalitions are self-enforcing: every pair of members mutually agree to cooperate with each other. The optimisation problem that agents face is forming coalitions to maximise their own ability while minimising the increase in their competitors’ ability. Representing the model in a n-dimensional Euclidean space and assuming perfect rationality, I analyse (1) The existence and type of equilibria attained (2) The necessary conditions for movement from the initial state (3) The effect of coalition formation on its members’ abilities and payoff. Section 4 of the paper develops an algorithmic process of coalition formation (APCF) to simulate an evolutionary mechanism of attaining equilibrium for agents lacking foresight.