Monetary payoff and utility function in adaptive learning models

This paper focuses on econometric issues, especially the common assumption that monetary payoff is subjects' actual utility, in estimating subjects' learning behaviors using experimental data. I propose a generalized adaptive learning model that nests commonly used learning rules. First, I show that for a wide range of model parameters, adding a constant to the utility function alters players' learning dynamics. Such a range includes commonly used learning models, such as experience-weighted attraction (EWA), payoff assessment and impulse-matching learning. This result implies that the usual treatment of monetary reward as the actual utility is potentially misspecified, in addition to the common concern of risk preference. To deal with such an issue, the econometric model specifies a player's utility as an unknown function of monetary payoff. It is estimated jointly with the generalized learning model. I show that they are jointly identified under weak conditions. Using the experimental dataset by Selten and Chmura (2008) and Chmura et al. (2012), I reject the null hypothesis that monetary payoffs are utility. Incorrectly imposing such a restriction substantially biases the learning parameters, especially the weight on forgone utility. In addition, when a generalized model is considered, subjects are found to depreciate the unchosen action's experience more than the chosen one. Consequently, they are more responsive to the unchosen action's recent utility, rather than that of the chosen one. This feature is absent in commonly used learning models, such as EWA.