This chapter examines resource allocation in an economy with increasing returns based on the concept of the core. Application of the core to the study of resource allocation with increasing returns was initiated by Herbert Scarf (1963) soon after the close relationship between the competitive equilibria and the core allocations of an exchange economy were first rigorously established. It seemed intuitive that if the possibility of exchange among agents can yield allocations that cannot be improved upon by any subgroup of agents left to its own resources, this property should be all the more true if, in addition to the possibility of exchanging goods, agents have access to a technique of production with increasing returns. On the basis of this intuition, Scarf had hoped to find an interesting way of decentralizing core allocations; however, the conjecture that core allocations exist under the general circumstances just described turned out to be false, or at least not true without restrictive conditions. To understand the concept of a core allocation, this chapter considers cooperative game theory.
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