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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Autores principales:	Pinasco, J.P., Rodríguez Cartabia, M., Saintier, N.
Formato:	JOUR
Materias:	Agent-based models Evolutionary games Wealth distribution
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_21530785_v8_n4_p874_Pinasco
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_21530785_v8_n4_p874_Pinasco2023-10-03T16:39:26Z A Game Theoretic Model of Wealth Distribution Pinasco, J.P. Rodríguez Cartabia, M. Saintier, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Pinasco, J.P. Rodríguez Cartabia, M. Saintier, N. 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.
format	JOUR
author	Pinasco, J.P. Rodríguez Cartabia, M. Saintier, N.
author_facet	Pinasco, J.P. Rodríguez Cartabia, M. Saintier, N.
author_sort	Pinasco, J.P.
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
url	http://hdl.handle.net/20.500.12110/paper_21530785_v8_n4_p874_Pinasco
work_keys_str_mv	AT pinascojp agametheoreticmodelofwealthdistribution AT rodriguezcartabiam agametheoreticmodelofwealthdistribution AT saintiern agametheoreticmodelofwealthdistribution AT pinascojp gametheoreticmodelofwealthdistribution AT rodriguezcartabiam gametheoreticmodelofwealthdistribution AT saintiern gametheoreticmodelofwealthdistribution
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A Game Theoretic Model of Wealth Distribution

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