Expectation Formation in an Evolving Game of Uncertainty: Theory and New Experimental Evidence

We examine the nature of stated subjective probabilities in a complex, evolving context in which true event probabilities are not within subjects' explicit information set. Specifically, we collect information on subjective expectations in a car race wherein participants must bet on a particular car but cannot influence the odds of winning once the race begins. In our setup, the actual probability of the good outcome (a win) can be determined based on computer simulations from any point in the process. We compare this actual probability to the subjective probability participants provide at three different points in each of 6 races. We find that the S-shaped curve relating subjective to actual probabilities found in prior research when participants have direct access to actual probabilities also emerges in our much more complex situation, and that there is only a limited degree of learning through repeated play. We show that the model in the S-shaped function family that provides the best fit to our data is Prelec's (1998) conditional invariant model.