# Bounded rationality and correlated equilibria

## Author

Listed:
• Fabrizio Germano

() (Universitat Pompeu Fabra)

• Peio Zuazo-Garin

() (University of the Basque Country (UPV/EHU))

## Abstract

Abstract We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players’ behavior deviates from rationality, but rather, on players’ higher-order beliefs about the frequency of such deviations. We assume that there exists a probability p such that all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information. Importantly, they can be applied to observed frequencies of play for arbitrary normal-form games to derive a measure of rationality $$\overline{p}$$ p ¯ that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization.

## Suggested Citation

• Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
• Handle: RePEc:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0547-5
DOI: 10.1007/s00182-016-0547-5
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## References listed on IDEAS

as
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Full references (including those not matched with items on IDEAS)

### Keywords

Strategic interaction; Correlated equilibrium; Robustness to bounded rationality; Approximate knowledge; Incomplete information; Measure of rationality; Experiments;

### JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
• D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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