V. Sasidevan, Deepak Dhar
We study a variation of the minority game, in which each agent uses a probabilistic strategy, and tries to optimize her total expected weighted future payoff, the weight of the payoff after $\tau$ days being $(1 - \lambda) \lambda^\tau$, with $\lambda < 1$. We show that standard Nash equilibrium concept is unsatisfactory in this case, and propose an alternative, called co-action equilibrium. We study the co-action equilibrium steady state of the system as $\lambda$ is varied from 0 to 1, and show that it gives a higher expected payoff than the Nash equilibrium for all agents. Parameters of the optimal strategy depend on $\lambda$, and can change discontinuously as $\lambda$ is varied, even for a finite number of agents. We analyse in detail the optimal strategies when the number of agents $N \leq 7$, and they decide selfishly, using only previous day's outcome.
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http://arxiv.org/abs/1212.6601
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