An Adaptive Learning Model with Foregone Payoff Information

Abstract

Abstract In this paper, we provide theoretical predictions on the long-run behavior of an adaptive decision maker with foregone payoff information. In the model, the decision maker assigns a subjective payoff assessment to each action based on his past experience and chooses the action that has the highest assessment. After receiving a payoff, the decision maker updates his assessments of actions in an adaptive manner, using not only the objective payoff information but also the foregone payoff information, which may be distorted. The distortion may arise from “the grass is always greener on the other side” effect, pessimism/optimism or envy/gloating; it depends on how the decision maker views the source of the information. We first provide conditions in which the assessment of each action converges, in that the limit assessment is expressed as an average of the expected objective payoff and the expected distorted payoff of the action. Then, we show that the decision maker chooses the optimal action most frequently in the long run if the expected distorted payoff of the action is greater than the ones of the other actions. We also provide conditions, under which this model coincides with the experience-weighted attraction learning, stochastic fictitious play and quantal response equilibrium models, and thus this model provides theoretical predictions for the models in decision problems.

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