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Jacob K. Goeree, Charles A. Holt and Thomas R. Palfrey

Quantal response equilibrium replaces the sharp best responses of standard game theory with smoothed “quantal” responses. This theory incorporates elements of stochastic choice originally developed by mathematical psychologists and statisticians into an equilibrium in which players’ beliefs that motivate decisions are consistent with the stochastic choices resulting from those decisions. This paper provides an introduction to quantal response models, with intuitive graphical representations that highlight connections to Nash equilibrium and level-k analysis in non-cooperative games. The analysis clarifies how standard (i.i.d.) error assumptions provide sharp, falsifiable predictions, even without specific distributional assumptions (logit, probit, etc.).The emphasis is on a coherent behavioral game theory that explains intuitive deviations from Nash equilibrium predictions in experimental games. This primer walks the reader through a series of examples illustrating the application of QRE theory to simple matrix games, multiplayer games, games with continuous strategy spaces, multistage games in extensive form, and Bayesian games.

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Lisa R. Anderson, Roland G. Fryer and Charles A. Holt

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Jacob K. Goeree, Charles A. Holt, Philippos Louis, Thomas R. Palfrey and Brian Rogers

Quantal response equilibrium (QRE) builds the possibility of errors into an equilibrium analysis of games. One objection to QRE is that specific functional forms must be chosen to derive equilibrium predictions. As these can be chosen from an infinitely dimensional set, another concern is whether QRE is falsifiable. Finally, QRE can typically only be solved numerically. We address these concerns through the lens of a novel set-valued solution concept, rank-dependent choice equilibrium (RDCE), which imposes a simple ordinal monotonicity condition: equilibrium choice probabilities are ranked the same as their associated expected payoffs. We first discuss important differences between RDCE and QRE and then show that RDCE envelopes all QRE models. Finally, we show that RDCE (and, hence, QRE) is falsifiable since the measure of the RDCE set, relative to the set of all mixed-strategy profiles, converges to zero at factorial speed in the number of available actions.