A Game Theoretic Model of Wealth Distribution

In this work, we consider an agent-based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero-sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study th...

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Detalles Bibliográficos
Publicado: 2018
Materias:
Agent-based models
Evolutionary games
Wealth distribution
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21530785_v8_n4_p874_Pinasco
http://hdl.handle.net/20.500.12110/paper_21530785_v8_n4_p874_Pinasco
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_21530785_v8_n4_p874_Pinasco
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spelling paper:paper_21530785_v8_n4_p874_Pinasco2023-06-08T16:34:22Z A Game Theoretic Model of Wealth Distribution Agent-based models Evolutionary games Wealth distribution In this work, we consider an agent-based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero-sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satisfies an equation close to the classical replicator equation. Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. For pure strategies equilibria, the wealth distribution is fixed after some transient time, and those players which initially were close to the optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coefficients of the game matrix. We compute theoretically their second moment in this case. © 2018, Springer Science+Business Media, LLC, part of Springer Nature. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21530785_v8_n4_p874_Pinasco http://hdl.handle.net/20.500.12110/paper_21530785_v8_n4_p874_Pinasco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Agent-based models
Evolutionary games
Wealth distribution
spellingShingle Agent-based models
Evolutionary games
Wealth distribution
A Game Theoretic Model of Wealth Distribution
topic_facet Agent-based models
Evolutionary games
Wealth distribution
description In this work, we consider an agent-based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero-sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satisfies an equation close to the classical replicator equation. Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. For pure strategies equilibria, the wealth distribution is fixed after some transient time, and those players which initially were close to the optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coefficients of the game matrix. We compute theoretically their second moment in this case. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
title A Game Theoretic Model of Wealth Distribution
title_short A Game Theoretic Model of Wealth Distribution
title_full A Game Theoretic Model of Wealth Distribution
title_fullStr A Game Theoretic Model of Wealth Distribution
title_full_unstemmed A Game Theoretic Model of Wealth Distribution
title_sort game theoretic model of wealth distribution
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21530785_v8_n4_p874_Pinasco
http://hdl.handle.net/20.500.12110/paper_21530785_v8_n4_p874_Pinasco
_version_ 1768542479236202496

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