  We generalize the Bush--Mosteller learning, the Roth--Erev learning, and the
social learning to include mistakes such that the nonlinear replicator-mutator
equation with either additive or multiplicative mutation is generated in an
asymptotic limit. Subsequently, we exhaustively investigate the ubiquitous
Rock-Paper-Scissors game for some analytically tractable motifs of mutation
pattern. We consider both symmetric and asymmetric game interactions, and
reveal that mistakes can some-times help the players learn. While the
replicator-mutator flow exhibits rich dynamics that include limit cycles and
chaotic orbits, it can control chaos as well to lead to rational Nash
equilibrium outcome. Moreover, we also report an instance of hitherto unknown
Hamiltonian structure of the replicator-mutator equation.
