A stochastic variant of replicator dynamics in zero-sum games and its invariant measures Article Swipe
Maximilian Engel
,
Georgios Piliouras
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2302.06969
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2302.06969
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.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2302.06969
- https://arxiv.org/pdf/2302.06969
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4321012680
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https://openalex.org/W4321012680Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2302.06969Digital Object Identifier
- Title
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A stochastic variant of replicator dynamics in zero-sum games and its invariant measuresWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-02-14Full publication date if available
- Authors
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Maximilian Engel, Georgios PiliourasList of authors in order
- Landing page
-
https://arxiv.org/abs/2302.06969Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2302.06969Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2302.06969Direct OA link when available
- Concepts
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Replicator equation, Mathematics, Invariant measure, Invariant (physics), Nash equilibrium, Axiom, Measure (data warehouse), Applied mathematics, Mathematical economics, Pure mathematics, Computer science, Ergodic theory, Population, Mathematical physics, Geometry, Sociology, Database, DemographyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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