Undecidability of the Existence of Pure Nash Equilibria

The purpose of this paper is to show that for any positive integer n, there exists no algorithm which decides for each non-cooperative n-person game in strategic form with partially computable payoff functions whether it has a pure Nash equilibrium or not.

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Bibliographic Details
Published in:Economic theory 2004-02, Vol.23 (2), p.423-428
Main Author: Sofronidis, N. E.
Format: Article
Language:English
Subjects:
Algorithms
Cooperation
Economic analysis
Economic theory
Economics
Equilibrium
Game theory
Games
Integers
Mathematical analysis
Mathematical functions
Mathematical theorems
Nash equilibrium
Natural numbers
Problem solving
Recursion
Recursion theory
Undecidability
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Description
Summary:The purpose of this paper is to show that for any positive integer n, there exists no algorithm which decides for each non-cooperative n-person game in strategic form with partially computable payoff functions whether it has a pure Nash equilibrium or not.
ISSN:0938-2259
1432-0479
DOI:10.1007/s00199-003-0394-z