Repository: Freie Universit├Ąt Berlin, Math Department

A stochastic variant of replicator dynamics in zero-sum games and its invariant measures

Engel, Maximilian and Piliouras, Georgios (2023) A stochastic variant of replicator dynamics in zero-sum games and its invariant measures. arXive . pp. 1-19. (Submitted)

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Official URL: https://doi.org/10.48550/arXiv.2302.06969

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
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:17 Apr 2023 09:40

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