On allocations attainable through Nash equilibria

Abstract

The purpose of this paper is to show that there are severe limitations on allocations attainable through mechanisms which can be viewed as Nash noncooperative games in which the agents’ messages constitute their strategies. In such mechanisms, the designer chooses the individual agents’ message sets and the rule (called outcomefunctionl) specifying the resource allocation resulting from the agents’ message choices. The messages chosen by agents constitute a Nash (noncooperative) equilibrium if no agent can unilaterally improve his situation as long as others do not change their messages. Clearly the equilibrium messages will depend on the agents’ characteristics (initial endowments, preferences, technology) and, hence, so will the allocations corresponding to these messages. We shall refer to the totality of all the agents’ characteristics as the environment and we shall call the allocations generated by Nash equilibrium messages Nash allocations. The relationship between environments and the corresponding Nash allocation sets specified by an outcome function constitutes the (Nash) performance correspondencea associated with that outcome function. The designer of the mechanism is assumed to be interested in the performance correspondence, but he can only control it indirectly by choosing the outcome function and the message sets. This paper shows that such indirect control is quite limited: only certain types of performance correspondences can be generated by a Nash equilibrium mechanism even if the designer has great freedom in selecting outcome functions and message sets. The economist’s interest in the design of resource allocating mechanisms