A study of choice correspondences in economies with a variable number of agents

We study correspondences defined over classes of exchange economies and associating with each element in the class a set of allocations at which resources are thought to be divided fairly among the agents. We formulate a series of axioms describing how correspondences could, or should, respond to certain changes in the number of agents. An example is: “If an allocation is optimal for some economy, then the replicated allocation is optimal for the replicated economy.” We identify which of these axioms are satisfied by the correspondences that have been proposed as solutions to the problem of fair division. We use the axioms, in conjunction with traditional axioms (such as efficiency), to characterize the Walrasian correspondence operated from equal division.