Experience-weighted Attraction Learning in Normal Form Games
Econometrica · 1999 · Volume 67 · Issue 4
Abstract
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 parameterδthat weights the strength of hypothetical reinforcement of strategies that werenotchosen 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,φandρ, 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. Whenδ= 0 andρ= 0, cumulative choice reinforcement results. Whenδ= 1 andρ=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 ofδare generally around .50,φaround .8 − 1, andρvaries from 0 toφ. 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.
Keywords
Learning, behavioral game theory, reinforcement learning, fictitious play.
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