Engel, Maximilian and Piliouras, Georgios
(2023)
*A stochastic variant of replicator dynamics in zero-sum games and its invariant measures.*
Physica D: Nonlinear Phenomena, 456
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Official URL: https://doi.org/10.1016/j.physd.2023.133940

## Abstract

We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the space of mixed strategies. Depending on the noise strength we can furthermore characterize these invariant measures by finding accumulation of mass at specific parts of the boundary. In particular, regardless of the magnitude of noise, we show that any invariant probability measure is a convex combination of Dirac measures on pure strategy profiles, which correspond to vertices/corners of the agents' simplices. Thus, in the presence of stochastic perturbations, even in the most classic zero-sum settings, such as Matching Pennies, we observe a stark disagreement between the axiomatic prediction of Nash equilibrium and the evolutionary emergent behavior derived by an assumption of stochastically adaptive, learning agents.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2936 |

Deposited By: | Monika Drueck |

Deposited On: | 17 Apr 2023 09:40 |

Last Modified: | 23 Jan 2024 12:53 |

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