In some economic games, participants systematically display behavior that departs from the model of payoff maximization, and this is usually attributed to social preferences. In this paper we focus on a new interactive context, a mixed-motive game called "Alternative Traveler's Dilemma" (ATD). In this context, most participants choose strictly dominated strategies. Preliminary studies suggest the reason for such a tendency is that participants have social preferences, usually competitive in nature. The question is whether some cognitive factors should also be included in models that account for the tendency at stake. More specifically, we investigate whether participants neglect payoff maximization, that is, whether they fail to notice that, by pursuing some competitive goal, they are not maximizing their payoffs. We report the results of an experiment that supports this hypothesis. We conclude that in order to explain anomalous behavior in the ATD, and similar games, we need to study the cognitive factors that bound participants' strategies and understanding of the game.