Prediction using Prospect Theory

In this report, we consider prediction of an agent’s preferences over risky monetary outcomes using Prospect Theory. We suppose that for a given agent we have data on previous prospects that the agent has accepted or declined. Based on this information, we would like to predict whether the agent will accept some new prospect X∗. This amounts to learning a value function v and probability weighting functions w, w− for the agent in question, and using these functions to establish whether the prospect will look attractive to them. In general, we do not expect to have sufficient data on a single agent to learn (v, w, w−) from scratch. Instead, we assume that we have a population of agents with observed decision histories, on which the algorithm may first be trained. Each training agent has different values for (v, w, w−). We assume an arbitrary parameterisation of these functions, controlled by some θ. Then, following the approach taken by Chajewska and Koller (2000) for prediction using Expected Utility Theory, we model θ as having some population-wide distribution P . Using P as a prior for the parameter value specific to the agent on whom we wish to make prediction, we may define a probability p∗ that the agent is someone who would accept X∗. We present an algorithm that uses a fully Bayesian framework to learn a posterior distribution for P , and hence a posterior distribution for p∗. This could be highly valuable in any competitive context where we expect an opponent to follow Prospect Theory, as it tells us which offers X∗ they are likely to accept. This approach differs from how PT is typically implemented in the literature. Most studies have been primarily descriptive and have sought to explain specific phenomena. Usually, heterogeneity in the functions (v, w, w−) features as random effects terms and the model is fit using Maximum Likelihood. Our algorithm is then made more robust by allowing a small proportion of agents to deviate from PT. That ensures that the posterior for P cannot be biased by a small number of training agents whose behaviour does not correlate with the predictions of PT. Further, if the agent on whom