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%2F60076658%3A12310%2F22%3A43904906" target="_blank" >RIV/60076658:12310/22:43904906 - 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&apos;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. © 2022, Journal of Dynamics and Games. All Rights Reserved.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

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

Name of the periodical

Journal of Dynamics and Games

ISSN

2164-6074

e-ISSN

2164-6074

Volume of the periodical

9

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

21

Pages from-to

351-371

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85141746052