### Abstract

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games.

Original language | English |
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Pages (from-to) | 1348-1377 |

Number of pages | 30 |

Journal | Mathematics of Operations Research |

Volume | 43 |

Issue number | 4 |

Early online date | 27 Jul 2018 |

DOIs | |

Publication status | Published - Nov 2018 |

### Keywords

- sample path large deviations
- evolutionary game theory
- stochastic stability
- Markov chains
- potential games
- congestion games
- STATIONARY DISTRIBUTIONS
- DIFFERENTIAL-EQUATIONS
- RECURSIVE ALGORITHMS
- LONG-RUN
- STABILITY
- EQUILIBRIA
- LIMITS

## Cite this

Sandholm, W. H., & Staudigl, M. (2018). Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics.

*Mathematics of Operations Research*,*43*(4), 1348-1377. https://doi.org/10.1287/moor.2017.0908