Interdependent preferences with a continuum of agents

We prove the existence of an equilibrium in exchange economies in which agents t form a finite measure space (T,T,μ), and the agents' preferences are interdependent. We introduce the notion of reference coalition C(t,p) for each t and for each price system p, which is simply the coalition of the agents who belong to a certain income range specified by t when p prevails in the market. The interdependent preferences of each agent t operate through the so-called “reference consumption vector η”, which represents the aggregate effect on t's preferences, resulting from varying consumption choices made by other agents. We choose for η the consumption vectors of the form 1/(μ[C(t,p)])∫C(t,p)x(s)dμ(s), where x is an assignment of commodity bundles and where the measure 1/(μ[C(t,p)])μ represents the relative frequencies of t coming into contact with each member of C(t,p). In view of the law of large numbers, the above integral can be interpreted as the “consumption trend” of the agents in C(t,p).