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Quantum games entropy

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  • Guevara Hidalgo, Esteban

Abstract

We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There exists a strong relationship between game theories, information theories and statistical physics. The density operator and entropy are the bonds between these theories. The analysis we propose is based on the properties of entropy, the amount of information that a player can obtain about his opponent and a maximum or minimum entropy criterion. The natural trend of a physical system is to its maximum entropy state. The minimum entropy state is a characteristic of a manipulated system, i.e., externally controlled or imposed. There exist tacit rules inside a system that do not need to be specified or clarified and search the system equilibrium based on the collective welfare principle. The other rules are imposed over the system when one or many of its members violate this principle and maximize its individual welfare at the expense of the group.

Suggested Citation

  • Guevara Hidalgo, Esteban, 2007. "Quantum games entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 797-804.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:797-804
    DOI: 10.1016/j.physa.2007.05.001
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    References listed on IDEAS

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    1. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    2. Richard McKelvey & Thomas Palfrey, 2015. "Erratum to: Quantal response equilibria for extensive form games," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 762-763, December.
    3. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
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