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The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widelystudied in terms of its theoretical analysis as well as in its applications,ranging from sociology and biology to economics. Many experimental results ofthe RPS game indicate that this game is better modelled by the discretizedbest-response dynamics rather than continuous time dynamics. In this work weshow that the attractor of the discrete time best-response dynamics of the RPSgame is finite and periodic. Moreover we also describe the bifurcations of theattractor and determine the exact number, period and location of the periodicstrategies.

Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game