Chapter 61 Logit Equilibrium Models of Anomalous Behavior: What to do when the Nash Equilibrium Says One Thing and the Data Say Something Else

Every experimentalist will sooner or later come across a situation in which results from initial baseline treatments conform nicely to the Nash equilibrium, but subsequent changes in parameters push the data in ways not predicted by Nash. This may happen when one begins by giving theory its best shot, reserving stress tests for later. Such tests often involve changing a parameter that, on the basis of intuition, is likely to alter behavior, but which has no effect on the Nash equilibrium. The dilemma is based on a situation in which two vacationers have purchased identical objects, which are then lost on the flight home. The airline tells them to fill out claim forms independently, with the promise that both claims will be paid if they match. Otherwise, both travelers are only reimbursed at the lower of the claims, with a small penalty for the high claimant and an equally small reward for the low claimant. Even with a very low penalty and reward, each person has an incentive to undercut any anticipated common claim amount, and so the only Nash equilibrium (in pure or mixed strategies) is at the lowest possible claim.