We discuss the strategy that rational agents can use to maximize their expected long-term\npayoff in the co-action minority game. We argue that the agents will try to get into a cyclic state,\nwhere each of the (2N + 1) agents wins exactly N times in any continuous stretch of (2N + 1)\ndays. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct\ncommunication between agents is not allowed, and only the publicly available common information\nis the record of total number of people choosing the first restaurant in the past. We determine\nexactly the average time required to reach the periodic state for this strategy. We show that it\nvaries as (N/ ln2)[1 + Ã?± cos(2Ãâ?¬ log2 N)], for large N, where the amplitude Ã?± of the leading term in\nthe log-periodic oscillations is found be 8Ãâ?¬2\n(ln 2)2 exp (âË?â??2Ãâ?¬2/ ln2) ââ?°Ë? 7 Ã?â?? 10âË?â??11.
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