Sure Or Not?

In this paper we investigate belief learning in repeated normal form games. We generalize the traditional expected utility function to allow subjects to hold a prior in-terval of beliefs rather than only a single prior belief point. We show that in this setting minimax strategies can be the strict best response in an ambiguous environment. We then apply our model to a zero-sum game experiment of sixty periods where subjects are incentivized to reveal prior belief intervals before each period. In our experiment reported interval lengths are significantly greater than zero, which supports the idea that subjects hold non-unique prior beliefs. In our first treatment, subjects choose pure strategies and realized outcomes are revealed to subjects before the next period. In the second treatment, subjects choose mixed strategies and both strategies and realized outcomes are revealed before the next period. Our treatments allow us to identify how subjects use information regarding strategies and realized outcomes to form beliefs. Contained in this paper there are three main findings:First, our generalized model verifies that minimax strategies can indeed strict best respond in ambiguous situations. This contributes to addressing the conundrum that, theoretically, in a normal form game choosing a mixed strategy is never the strict best response. There is, however, abundant evidence that people do in fact act in a random manner in strategic situations. Also, experimental data shows that subjects adopt non-unique prior when playing games. Through the analysis of belief sequences, we conclude that subjects are sophisticated in that they tend to use the strategy of their opponent to form beliefs when available. Finally, we demonstrate that for most subjects, interval lengths shrink to a steady state as the game proceeds.