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Strategy switches and co-action equilibria in a minority game

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  • Sasidevan, V.
  • Dhar, Deepak

Abstract

We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, N agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off 1, others zero. The agents optimize the expectation value of their discounted future pay-off, the discount parameter being λ. We propose an alternative to the standard Nash equilibrium, called co-action equilibrium, which gives higher expected pay-off for all agents. The optimal choice of probabilities of different actions are determined exactly in terms of simple self-consistent equations. The optimal strategy is characterized by N real parameters, which are non-analytic functions of λ, even for a finite number of agents. The solution for N≤7 is worked out explicitly indicating the structure of the solution for larger N. For large enough future time horizon, the optimal strategy switches from random choice to a win-stay lose-shift strategy, with the shift probability depending on the current state and λ.

Suggested Citation

  • Sasidevan, V. & Dhar, Deepak, 2014. "Strategy switches and co-action equilibria in a minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 306-317.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:306-317
    DOI: 10.1016/j.physa.2014.02.007
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
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    Cited by:

    1. Shu-Heng Chen & Umberto Gostoli, 2017. "Coordination in the El Farol Bar problem: The role of social preferences and social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 59-93, April.
    2. Hardik Rajpal & Deepak Dhar, 2018. "Achieving Perfect Coordination amongst Agents in the Co-Action Minority Game," Games, MDPI, vol. 9(2), pages 1-13, May.

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