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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10602 - Biology (theoretical, mathematical, thermal, cryobiology, biological rhythm), Evolutionary biology

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Dynamics and Games

ISSN

2164-6066

e-ISSN

2164-6074

Svazek periodika

9

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

351-371

Kód UT WoS článku

000720317100001

EID výsledku v databázi Scopus

2-s2.0-85141746052