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Complete stability of noncooperative games

  • D. G. Luenberger
Contributed Papers

Abstract

This paper is concerned with a class of noncooperative games ofn players that are defined byn reward functions which depend continuously on the action variables of the players. This framework provides a realistic model of many interactive situations, including many common models in economics, sociology, engineering, and political science. The concept of Nash equilibrium is a suitable companion to such models.

A variety of different sufficient conditions for existence, uniqueness, and stability of a Nash equilibrium point have been previously proposed. By sharpening the noncooperative aspect of the framework (which is really only implicit in the original framework), this paper attempts to isolate one set of “natural” conditions that are sufficient for existence, uniqueness, and stability. It is argued thatl quasicontraction is such a natural condition. The concept of complete stability is introduced to reflect the full character of noncooperation. It is then shown that, in the linear case, the condition ofl quasicontraction is both necessary and sufficient for complete stability.

Key Words

Game theory stability contraction mappings 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • D. G. Luenberger
    • 1
  1. 1.Department of Engineering-Economic SystemsStanford UniversityStanford

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