Learning models for the prisoner’s dilemma game: A review

Abstract

The paper provides a review of mathematical learning models for gaming behavior in sequences of prisoner’s dilemma games. The introductory part of the paper gives some basic information about the mathematics of traditional learning models. Three types of models are explained: Linear operator models, choice models and Markov-models. In the first part classical learning models for overt gaming behavior are presented. They were developed by Anatol Rapoport and his co-workers. Results for two Markov-models and a linear operator model are discussed. Van der Sanden developed a Markov-model with two latent value states and a transitional intermediate state. This model is based on earlier work of Meeker. Micko, Brückner und Ratzke developed a linear operator model with two latent dimensions called “cooperative inclination” and “trust”. The basic ideas of this model are very similar to Pruitt and Kimmel’s goal-expectation theory. Schulz and co-workers developed a series of learning models which account for players’ expectations and separate social value parameters and information processing parameters. In the most recent model of this type goals, expectations, and choices are overt variables. This model allows empirical tests of the goal expectation theory.