Quantal response equilibria for extensive form games

Abstract

This paper investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal choice model, and assume other players do so as well. We define an Agent Quantal Response Equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal choice probabilities are given by logit response functions.AQRE makes predictions that contradict the invariance principle in sys tematic ways. We show that these predictions match up with some exper imental findings by Schotter, Weigelt and Wilson (1993) about the play of games that differ only with lcspect to inessential transformations of the ex tensive form. The logit-AQRE also implies a unique selection from the set of subgame perfect equilibria in generic extensive form games. We examine data from signalling game experiments by Banks, Camerer, and Porter (1994) and Brandts and Holt (1993) . We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these ex periments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment.

The effects of payoff magnitude and heterogeneity on behavior in 2×2 games with unique mixed strategy equilibria

“…5For a formal and more detailed explanation of QRE, see McKelvey and Palfrey (1995, 1998. Those papers also provide discussion about the conceptual interpretation of,\.…”

External validation of voter turnout models by concealed parameter recovery

“…We intend to pursue this avenue of research in future work. 21 Note that this is about twice the subsidy based on the naive calculation corresponding to shifting the voting cost distribution down by 10% of  ( = 06 or 08, depending on the model). 22 The subsidy is equal to 64 according to the naive calculation.…”

“…21 In contrast, the policy recommendation based on the estimated ethical model entails a much larger subsidy, equal to 143 according to the equilibrium calculation. 22 This is eleven times the subsidy recommended by the other three models to achieve the same target.…”

“…Following McFadden (1981), we take the distribution of taste shocks to be specified by an extreme value distribution, leading to choice probabilities that are logit functions. As is now standard in the use of logit models in games, the quantal response component becomes part of the equilibrium (McKelvey and Palfrey (1995Palfrey ( , 1998). Hence, for each model, we characterize its logit quantal response equilibrium (LQRE), which represents the basis for estimation.…”

Introduction to Experimental Game Theory

“…Camerer et al distinguish the models' observable implications and compare them econometrically, finding that the strategic teaching model outperforms the equilibrium reputation model in the trust games. 19 19 In estimating the equilibrium reputation model, they allow for the noisiness of subjects' decisions using McKelvey and Palfrey's [28] extensive-form quantal response equilibrium.…”