Nash equilibria in random games with right fat-tailed distributions-张培刚发展研究院

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) } in a random m\times n asymmetric game and approximately n/2 in a random n\times 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.

ISSN号：1432-1270

链接：Nash equilibria in random games with right fat-tailed distributions | International Journal of Game Theory (springer.com)