Using chemical reaction network theory to show stability of distributional dynamics in game theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60077344%3A_____%2F22%3A00549277" target="_blank" >RIV/60077344:_____/22:00549277 - isvavai.cz</a>
Result on the web
<a href="https://www.aimsciences.org/article/doi/10.3934/jdg.2021030" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/jdg.2021030</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/jdg.2021030" target="_blank" >10.3934/jdg.2021030</a>

Result language
angličtina
Original language name
Using chemical reaction network theory to show stability of distributional dynamics in game theory
Original language description
This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy-Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10602 - Biology (theoretical, mathematical, thermal, cryobiology, biological rhythm), Evolutionary biology

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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