In Economics and Social Sciences Working Papers Series Nash Program

This article is a brief survey on the Nash program for coalitional games. Results of noncooperative implementation of the Nash solution, the Shapley value and the core are discussed. Journal of Economic Literature classification: C7. Nash program In game theory this is the name given to a research agenda, initiated in Nash (1953), intended to bridge the gap between the cooperative and non-cooperative approaches to the discipline. Many authors have contributed to the program since its beginnings (the reader is referred to Serrano (2005) for a comprehensive survey). The current article will concentrate on a few salient contributions. One should begin by introducing some preliminaries and providing definitions of some basic concepts, extensions of which may be also found in other entries of the dictionary, such as those corresponding to non-cooperative games, coalitional games, the core, the Shapley value or bargaining. 1. Preliminaries. The non-cooperative approach to game theory provides a rich language and develops useful tools to analyze strategic situations. One clear advantage of the approach is that it is able to model how specific details of the interaction may impact the final outcome. One limitation, however, is that its predictions may be highly sensitive to those details. For this reason it is worth also analyzing more abstract approaches that attempt to obtain conclusions that are independent of such details. The cooperative approach is one such attempt. Here are the primitives of the basic model in cooperative game theory. Let N = {1, . . . , n} be a finite set of players. For each S, a non-empty subset of N , we shall specify a set V (S) containing |S|dimensional payoff vectors that are feasible for coalition S. Thus, a reduced form approach is taken because one does not explain what strategic choices are behind each of the payoff vectors in V (S). In addition, in this formulation, referred to as the characteristic function, it is implicitly assumed that the