We call into question game theory, as a account of how people play two player zero-sum games. Evidence from a modified version of the game Paper, Rock, Scissors suggests that people do not play randomly, and not according to certain play probabilities. We investigated the relationship between game theory predictions and a cognitive model of game playing based on the detection of sequential dependencies. Previous research has shown that the sequential dependency model can account for a number of empirical findings that game theory cannot. The sequential dependency model has been implemented using both simple neural networks and ACT-R. In this paper we used simple neural networks (a description of how our findings relate to the ACT-R model is included in the Conclusion section). For simple games, such as Paper, Rock, Scissors, game theory has been able to correctly predict aggregate move probabilities. In this paper we show that this is an artifact of the symmetry of the payoffs, and that for asymmetrical payoffs the game theory solution does not predict human behavior. Furthermore, we show that the model of game playing that underlies game theory cannot be used to predict the results no matter what move probabilities are used. Finally, we show that the results can be accounted for by augmenting the network sequential dependency model so that the reward system is related to the game payoffs.