Remarks on Nash Equilibria for Games with Additively Coupled Payoffs

If the payoffs of a game are affine, then they are additively coupled. In this situation both the Weierstrass theorem and the Bauer maximum principle can be used to produce existence results for a Nash equilibrium, since each player is faced with an individual, independent optimization problem. We c...

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Bibliographic Details
Published in:Economic theory 1997-01, Vol.9 (1), p.161-167
Main Author: Balder, Erik J.
Format: Article
Language:English
Subjects:
Differential games
Economic behaviour
Equilibrium models
Exposita Notes
Game theory
Games
Mathematical functions
Mathematical triviality
Maximum principle
Nash equilibrium
Probabilities
Space based observatories
Topological theorems
Topological vector spaces
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Summary:If the payoffs of a game are affine, then they are additively coupled. In this situation both the Weierstrass theorem and the Bauer maximum principle can be used to produce existence results for a Nash equilibrium, since each player is faced with an individual, independent optimization problem. We consider two instances in the literature where these simple observations immediately lead to substantial generalizations.
ISSN:0938-2259
1432-0479
DOI:10.1007/bf01213450