Achieving perfect coordination amongst agents in the co-action minority game

Abstract

We discuss the strategy that rational agents can use to maximize their expected long-term payoff in the co-action minority game. We argue that the agents will try to get into a cyclic state, where each of the $(2N+1)$ agent wins exactly $N$ times in any continuous stretch of $(2N+1)$ days. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct communication between agents is not allowed, and only the publicly available common information is the record of total number of people choosing the first restaurant in the past. We determine exactly the average time required to reach the periodic state for this strategy. We show that it varies as $(N/\ln 2)[1+\alpha \cos (2\pi {\log }_{2}N)$], for large $N$, where the amplitude $\alpha$ of the leading term in the log-periodic oscillations is found be $\frac{8{\pi }^2}{(\ln 2{)}^2}\exp (-2{\pi }^2/\ln 2)\approx 7\times 10^{-11}$.

arXiv commentAdded additional discussion, and a figure

References in corpus (7)

• Emergence of Cooperation and Organization in an Evolutionary Game
• The Kolkata Paise Restaurant Problem and Resource Utilization
• Spatial Log Periodic Oscillations of First-Passage Observables in Fractals
• Cooperation amongst competing agents in minority games
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Cited by in corpus (1)

• Achieving Maximum Utilization in Optimal Time for Learning or Convergence in the Kolkata Paise Restaurant Problem