Nash equilibria in random games with right fat-tailed distributions
Ting Pei (peterpeiting@hotmail.com) and
Satoru Takahashi
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Ting Pei: Huazhong University of Science and Technology
International Journal of Game Theory, 2023, vol. 52, issue 4, No 8, 1153-1177
Abstract:
Abstract We study the distribution of the number of mixed strategy Nash equilibria in two-player games where each player’s payoffs are independently drawn from an identical distribution. When the payoff distributions are sufficiently right fat-tailed, we characterize the Nash equilibria by best reply cycles of pure strategies, and we show that the expected number of Nash equilibria is approximately $$\sqrt{\pi mn/\left( m+n\right) }$$ π m n / m + n in a random $$m\times n$$ m × n asymmetric game and approximately n/2 in a random $$n\times n$$ n × n symmetric game. We also provide new lower bounds for the expected number of Nash equilibria in a random game with any type of payoff distribution.
Keywords: Random game; Number of equilibria; Best response cycles; Point rationalizability (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00182-023-00863-2
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