Satisficing game theory offers an alternative to classical game theory that describes a flexible model of players' social interactions. Players' utility functions depend on other players' attitudes rather than simply their actions. However, satisficing players with conflicting attitudes may enact dysfunctional behaviors, which results in poor performance. We present an evolutionary method by which a population of players may adapt their attitudes to improve payoff. In addition, we extend the Nash-equilibrium concept to satisficing games, showing that the method leads players toward the equilibrium in their attitudes. We apply these ideas to the stag hunt--a simple game in which cooperation does not easily evolve from noncooperation. The evolutionary method provides two major contributions. First, satisficing players may improve their performance by adapting their attitudes. Second, numerical results demonstrate that cooperation in the stag hunt can emerge much more readily under the method we present than under traditional evolutionary models.