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Experience-weighted Attraction Learning in Normal Form Games

Econometrica 1999 67(4), 827-874
In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do.

Peer-Induced Fairness in Games

American Economic Review 2009 99(5), 2022-2049
People exhibit peer-induced fairness concerns when they look to their peers as a reference to evaluate their endowments. We analyze two independent ultimatum games played sequentially by a leader and two followers. With peer-induced fairness, the second follower is averse to receiving less than the first follower. Using laboratory experimental data, we estimate that peer-induced fairness between followers is two times stronger than distributional fairness between leader and follower. Allowing for heterogeneity, we find that 50 percent of subjects are fairness-minded. We discuss how peer-induced fairness might limit price discrimination, account for low variability in CEO compensation, and explain pattern bargaining.