## Abstract

The Lipschitz constant of a game measures the maximal amount of influence that one player has on the payoff of some other player. The worst-case Lipschitz constant of an n-player k-action δ-perturbed game, λ(n, k, δ) , is given an explicit probabilistic description. In the case of k≥ 3 , it is identified with the passage probability of a certain symmetric random walk on Z. In the case of k= 2 and n even, λ(n, 2 , δ) is identified with the probability that two i.i.d. binomial random variables are equal. The remaining case, k= 2 and n odd, is bounded through the adjacent (even) values of n. Our characterization implies a sharp closed-form asymptotic estimate of λ(n, k, δ) as δn/ k→ ∞.

Original language | English |
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Pages (from-to) | 293-306 |

Number of pages | 14 |

Journal | International Journal of Game Theory |

Volume | 51 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2022 |

## Keywords

- Anonymous games
- Approximate Nash equilibrium
- Large games
- Perturbed games

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics (miscellaneous)
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty