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We generalize the Bush--Mosteller learning, the Roth--Erev learning, and thesocial learning to include mistakes such that the nonlinear replicator-mutatorequation with either additive or multiplicative mutation is generated in anasymptotic limit. Subsequently, we exhaustively investigate the ubiquitousRock-Paper-Scissors game for some analytically tractable motifs of mutationpattern. We consider both symmetric and asymmetric game interactions, andreveal that mistakes can some-times help the players learn. While thereplicator-mutator flow exhibits rich dynamics that include limit cycles andchaotic orbits, it can control chaos as well to lead to rational Nashequilibrium outcome. Moreover, we also report an instance of hitherto unknownHamiltonian structure of the replicator-mutator equation.

Replicator-mutator dynamics of Rock-Paper-Scissors game: Learning through mistakes