Neuroeconomic models take economic theory literally, interpreting hypothesized quantities as observables in the brain in order to provide insight into choice behaviour. This thesis develops a model of the neural decision process in strategic games with a unique mixed strategy equilibrium. In such games, players face both an incentive to best-respond to valuations and to act unpredictably. Similarly, we model choice as the result of the interaction between action value and the noise inherent in networks of spiking neurons. Our neural model generates any ratio of choices through the specification of action value, including the equilibrium ratio, and provides an explanation for why we observe equilibrium behaviour in some contexts and not others. The model generalizes to a random-utility model which gives a structural specification to the error term and makes action value observable in the spike rates of neurons. Action value is measured in the spike activity of the Superior Colliculus (SC) while monkeys play a saccade version of matching pennies. We find SC activity predicts upcoming choices and is influenced by the history of events in the game, correlating with a behaviourally-established model of learning, and choice simulations based on neural measures of value exhibit similar biases to our behavioural data. A neural measure of value yields a glimpse at how valuations are updated in response to new information and compared stochastically, providing us with unique insight into modelling choice in strategic games. / Thesis (Ph.D, Economics) -- Queen's University, 2011-06-14 14:48:36.226