  We examine the effects of memory and different updating paradigms in a
game-theoretic model of competitive learning, where agents are influenced in
their choice of strategy by both the choices made by, and the consequent
success rates of, their immediate neighbours. We apply parallel and sequential
updates in all possible combinations to the two competing rules, and find,
typically, that the phase diagram of the model consists of a disordered phase
separating two ordered phases at coexistence. A major result is that the
corresponding critical exponents belong to the generalised universality class
of the voter model. When the two strategies are distinct but not too different,
we find the expected linear response behaviour as a function of their
difference.Finally, we look at the extreme situation when a superior strategy,
accompanied by a short memory of earlier outcomes, is pitted against its
inverse; interestingly, we find that a long memory of earlier outcomes can
occasionally compensate for the choice of a globally inferior strategy.

Physics and Society;Statistical Mechanics