  We propose a stochastic model in evolutionary game theory where individuals
(or subpopulations) can mutate changing their strategies randomly (but rarely)
and explore the external environment. This environment affects the selective
pressure by modifying the payoff arising from the interactions between
strategies. We derive a Fokker-Plank integro-differential equation and provide
Monte-Carlo simulations for the Hawks vs Doves game. In particular we show
that, in some cases, taking into account the external environment favors the
persistence of the low-fitness strategy.
