The limit distribution of pure strategy Nash equilibria in symmetric bimatrix games -- Web of Science 5.0

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The limit distribution of pure strategy Nash equilibria in symmetric bimatrix games
Stanford W
MATHEMATICS OF OPERATIONS RESEARCH 21 (3): 726-733 AUG 1996

Document type: Article

Language: English

Cited References: 9

Times Cited: 3

Abstract:
In a ''random'' symmetric bimatrix game, let X and Y represent the numbers of symmetric and asymmetric pure strategy Nash equilibria occurring, respectively. We find the probability distributions of both X and Y depending on m, the number of pure strategies for each of the two players. We show the distribution of X approaches the Poisson distribution with mean one and the distribution of 1/2 Y approaches the Poisson distribution with mean 1/2 as m increases. We determine the joint distribution of X and Y and the limit distribution of X + Y. From this we see the probability of at least one pure strategy Nash equilibrium approaches 1 - e(-1.5) approximate to .7769 as m increases. For general bimatrix games, the corresponding limit of probabilities is 1 - e(-1) approximate to .6321. Thus in this sense, pure strategy Nash equilibria are seen to be significantly more common under the condition of symmetry than otherwise.

Author Keywords:
bimatrix game, Nash equilibria

KeyWords Plus:
N-PERSON GAMES

Addresses:
Stanford W, UNIV ILLINOIS,DEPT ECON MC144,601 S MORGAN ST,ROOM 2103,CHICAGO,IL 60607

Publisher:
INST OPERATIONS RESEARCH MANAGEMENT SCIENCES, LINTHICUM HTS

IDS Number:
VV423

ISSN:
0364-765X

Article 21 of 40

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