Response functions

Imagine that John must choose between two uncertain payoff distributions, knowing that the set of possible payoffs is the same for both, but nothing about the shapes of the distributions. In the first period he chooses either alternative and experiences a payoff as a result of his choice. Given this experienced payoff, in the second period he decides whether to choose the same alternative again, or switch. We model John’s second period choice with a response function, i.e., a mapping from obtained payoffs to the probability of choosing the same alternative in the second period. We first provide results on (i) how the shape of the response function affects both expected payoffs and exposure to risk, and (ii) what standard models of choice under uncertainty would predict about the shape of the response function. We then run an experiment to elicit subjects’ response functions, empirically characterize the heterogeneity across subjects with a mixture model, and illustrate how payoffs vary across response function types. Finally, we use our theoretical results, along with additional information that we collected from subjects, to interpret their response functions.