Satisficing game theory is an alternative to traditional non-cooperative game theory which offers increased flexibility in modeling players' social interactions. However, satisficing players with conflicting attitudes may implement dysfunctional behaviors, leading to poor performance. In this thesis, we present two attempts to "bridge the gap" between satisficing and non-cooperative game theory. First, we present an evolutionary method by which players adapt their attitudes to increase raw payoff, allowing players to overcome dysfunction. We extend the Nash equilibrium concept to satisficing games, showing that the evolutionary method presented leads the players toward an equilibrium in their attitudes. Second, we introduce the conditional utility functions of satisficing theory into an otherwise traditional non-cooperative framework. While the conditional structure allows increased social flexibility in the players' behaviors, players maximize individual utility in the traditional sense, allowing us to apply the Nash equilibrium. We find that, by adjusting players' attitudes, we may alter the Nash equilibria that result.