Paying attention to payoffs in analogy-based learning

The analogy-based expectation equilibrium, or simply analogy equilibrium (AE), analyzes equilibrium stereotypes by imposing consistency of infinitely large action samples with the expectation that broad classes of opponent types behave identically. This paper introduces the payoff-confirming analogy equilibrium (PAE) to refine the set of analogy equilibria. The concept imposes additionally that sample marginal of own payoffs be consistent with one’s
expectations. Robust incorrect equilibrium stereotypes, i.e. non-Bayesian Nash PAE are shown to exist. General conditions are given for the prevalence of such stereotypes under correct expectations on exogenous uncertainty. In monotone selection games susceptible to winner’s curse, naive behavioral equilibrium leading to aggravation of adverse selection has been shown to match plausible informational assumptions of experienced, but behaviorally
biased, equilibrium play. Here, behavioral equilibrium is matched with a corresponding PAE with an incorrect prior and correct prior is shown to imply correct overall expectations.