A Game Theoretic Model of Wealth Distribution
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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.
KeywordsWealth distribution Evolutionary games Agent-based models
Mathematics Subject Classification91A22 91B69 91B60
This paper was partially supported by Grants UBACyT 20020130100283BA, CONICET PIP 11220150100032CO and ANPCyT PICT 2012-0153. J. P. Pinasco and N. Saintier members of CONICET. M. Rodríguez Cartabia is a Fellow of CONICET.
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