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Quantum Replicator Dynamics

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  • Guevara Hidalgo, Esteban

Abstract

We propose quantization relationships which would let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. The quantum version of the replicator dynamics is the equation of evolution of mixed states from quantum statistical mechanics. A system and all its members will cooperate and rearrange its states to improve their present condition. They strive to reach the best possible state for each of them which is also the best possible state for the whole system. This led us to propose a quantum equilibrium in which a system is stable only if it maximizes the welfare of the collective above the welfare of the individual. If it is maximized the welfare of the individual above the welfare of the collective the system gets unstable and eventually it collapses.

Suggested Citation

  • Guevara Hidalgo, Esteban, 2006. "Quantum Replicator Dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 393-407.
    • Handle: RePEc:eee:phsmap:v:369:y:2006:i:2:p:393-407
    DOI: 10.1016/j.physa.2006.02.017
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    References listed on IDEAS

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    1. Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2003. "Interference of quantum market strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 516-528.
    2. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    3. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle," Departmental Working Papers 8, University of Bialtystok, Department of Theoretical Physics.
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    Cited by:

    1. Griffin, Christopher, 2021. "The replicator dynamics of zero-sum games arise from a novel poisson algebra," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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