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A Game Theoretic Model of Wealth Distribution

Author

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  • Juan Pablo Pinasco

    (Universidad de Buenos Aires, Instituto de Matemática Santaló (IMAS), UBA-CONICET)

  • Mauro Rodríguez Cartabia

    (Universidad de Buenos Aires, Instituto de Matemática Santaló (IMAS), UBA-CONICET)

  • Nicolas Saintier

    (Universidad de Buenos Aires, Instituto de Matemática Santaló (IMAS), UBA-CONICET)

Abstract

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.

Suggested Citation

  • Juan Pablo Pinasco & Mauro Rodríguez Cartabia & Nicolas Saintier, 2018. "A Game Theoretic Model of Wealth Distribution," Dynamic Games and Applications, Springer, vol. 8(4), pages 874-890, December.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:4:d:10.1007_s13235-018-0240-3
    DOI: 10.1007/s13235-018-0240-3
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    References listed on IDEAS

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    1. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).

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