Learning What is Similar: Precedents and Equilibrium Selection

We argue that a precedent is important not only because it changes the relative frequency of a certain event, making it positive rather than zero, but also because it changes the way that relative frequencies are weighed. Specifically, agents assess probabilities of future events based on past occurrences, where not all of these occurrences are deemed equally relevant. More similar cases are weighed more heavily than less similar ones. Importantly, the similarity function is also learnt from experience by "second-order induction". The model can explain why a single precedent affects beliefs above and beyond its effect on relative frequencies, as well as why it is easier to establish reputation at the outset than to re-establish it after having lost it. We also apply the model to equilibrium selection in a class of games dubbed "Statis- tical Games", suggesting the notion of Similarity-Nash equilibria, and illustrate the impact of precedents on the play of coordination games.