Coalition Formation with Heterogeneous Agents
The paper analyzes a game of coalition formation in which agents with limited computational abilities possess heterogeneous endowments and seek to coax lesce into groups to produce and divide an output. The basic game is modelled as a two stage game; in t
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Introduction
The formation of coalitions is a common aspect of many economic activities; for example scientific research groups, consumers' associations, production partnerships, consumption and production cooperatives are all instances of voluntary agreements among independent parties that coalesce to obtain the same goal. Coalition formation has already been observed and studied in a number of works from different points of view: among these, Guesnerie and Oddou (1988) deals with the problem of coalition formation for the provision of public goods, Farrell and Scotchmer (1988) discusses formation of cooperatives of workers with different working capacity, while Bennet (1985) analyzes coalition formation in more general settings (see Greenberg (1994) for an excellent review).l In these works the formation of cooperating groups is affected by a moral hazard problem whenever private actions cannot be monitored. A common finding is that the cooperative agreement is self-sustained if the coalition 1
A large part of coalition formation literature is interested in games with externality, see for example Yi (1997) and Thoron (1998).
A. Kirman et al. (eds.), Economics with Heterogeneous Interacting Agents © Springer-Verlag Berlin Heidelberg 2001
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size is below a certain threshold, whereas it would not be incentive compatible in larger coalitions. These conclusions are in agreement with Olson (1983) (see also Ecchia and Mariotti (1998) and Yi (1997)}.
In this paper we analyze a game of coalition formation in which agents have heterogeneous endowments and try to coalesce into groups to produce and divide an output; the formation of a coalition does not affect the utilities of agents not belonging to such coalition (Le. this is a game without externalities). There is an incentive to aggregation due to an increasing returns to scale technology, but imperfect information on other agents' actions does not allow for the formation of a unique coalition in which all agents participate. Agents are not free to join an existing coalition without the consensus of its members (i.e. we consider an exclusive membership game, see Block (1996»2. The basic game is modelled as a two stage game; in the first stage every agent sends the other agents messages consisting in the proposal of a coalition; this allows individuals to identify which other individuals are willing to coalesce with them and therefore to coordinate their strategies. In the second stage, knowing the coalitions resulting from the coordination achieved in the first stage, agents choose which actions to perform; the resulting output is then divided among the members of the coalitions that have been formed. In this framework we show that there exists at least a Strong Nash equilibrium (SNE) characterized by the consecutive property, i.e. the richest agents form a coalition among themselves, and so do the poorest agents. One of the main aims of the paper is to verify whether, in a dynamic context in which the game is repeatedly played, this is the
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