Strategy switches and co-action equilibria in a minority game
AbstractWe 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 $\lambda$.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1212.6601.
Date of creation: Dec 2012
Date of revision: Sep 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-07 (All new papers)
- NEP-CSE-2013-01-07 (Economics of Strategic Management)
- NEP-GTH-2013-01-07 (Game Theory)
- NEP-MIC-2013-01-07 (Microeconomics)
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