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Pure $\epsilon$-equilibrium in random games

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  • Bary S. R. Pradelski
  • Bassel Tarbush

Abstract

We show that for any $\epsilon>0$ the probability that a randomly drawn game has a pure $\epsilon$-equilibrium goes to 1 as the number of agents gets large. This contrasts sharply with the known fact that if $\epsilon = 0$, that is, for pure Nash equilibrium, the probability is asymptotically $1- 1/e\approx 0.63$.

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  • Bary S. R. Pradelski & Bassel Tarbush, 2025. "Pure $\epsilon$-equilibrium in random games," Papers 2502.07585, arXiv.org.
    • Handle: RePEc:arx:papers:2502.07585
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    References listed on IDEAS

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    1. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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