Large deviations and multinomial probit choice

We consider a discrete choice model in which the payoffs to each of an agent’s n actions are subjected to the average of m i.i.d. shocks, and use tools from large deviations theory to characterize the rate of decay of the probability of choosing a given suboptimal action as m approaches infinity. Our model includes the multinomial probit model of Myatt and Wallace (2003) as a special case. We show that their formula describing the rates of decay of choice probabilities is incorrect, provide the correct formula, and use our large deviations analysis to provide intuition for the difference between the two.