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# Strategy switches and co-action equilibria in a minority game

Listed:
• V. Sasidevan
• Deepak Dhar

## 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 $\lambda$. 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 $\lambda$, even for a finite number of agents. The solution for $N \leq 7$ 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 $\lambda$.

## Suggested Citation

• V. Sasidevan & Deepak Dhar, 2012. "Strategy switches and co-action equilibria in a minority game," Papers 1212.6601, arXiv.org, revised Feb 2014.
• Handle: RePEc:arx:papers:1212.6601
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File URL: http://arxiv.org/pdf/1212.6601

## Citations

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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.

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