Abstract

The Nash program is an important research agenda initiated in Nash (1953) in order to bridge the gap between the noncooperative and cooperative counterparts of game theory. The program is thus turning sixty-seven years old, but I will argue it is not ready for retirement, as it is full of energy and one can still propose important directions to be explored. This paper completes and updates previous surveys, and suggests several directions for future research.

Highlights

  • The Nash program is an important research agenda initiated in Nash (1953)

  • (a) some results are obtained as limits are taken and some are exact implementations; (b) some results are proved under the assumption of complete information, others are written for incomplete information environments; (c) some assume that the number of players is fixed, and others take as parameters the number of players on each side of the bargaining table; (d) some assume a continuum of alternatives and others a finite set of alternatives; and so on

  • (i) As pointed out above, among all the leading game-theoretic solution concepts, the von Neumann–Morgenstern stable set remains virtually unexplored in the Nash program

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Summary

Introduction

The Nash program is an important research agenda initiated in Nash (1953). It is intended to bridge the gap between the noncooperative and cooperative counterparts of game theory. A rough count of papers in the Nash program, cited here and published or listed as working papers since my previous survey in 2005, is the following:. Many results can be found in the several decades of the program, and the reader is referred to Serrano (2005, 2008, 2014) for complementary surveys and commentaries. This paper completes and updates these previous pieces, and suggests several directions for future research. Given that I see this paper as a new chapter in the saga of previous surveys I have written on the subject, I will spare the reader of the section on preliminaries that introduces mathematical notation. As is always the case in surveys, the list of papers mentioned here will be incomplete and I apologize in advance to the authors of those worthy contributions that surely I will have missed

Interpretations and new directions
Recent contributions
The Nash solution
Other solutions to pure bargaining problems
Games in characteristic-function form
Incomplete-information environments
Other domains
Concluding remarks
Compliance with ethical standards
Full Text
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