A Bayesian Sequential Experimental Study of Learning in Games

El‐Gamal, Mahmoud A.; McKelvey, Richard D.; Palfrey, Thomas R.

doi:10.1080/01621459.1993.10476292

Cited by 31 publications

(10 citation statements)

References 12 publications

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“…Note that beliefs generally depend on a player's own type. 6 As we show later in the section, this provides a framework for linking HQRE approaches with cognitive hierarchy approaches, which share a similar feature of belief heterogeneity. This difference in beliefs results in equilibrium strategies (and induced mixed 4 While the assumptions of the F i above preclude this case, it can be approximated arbitrarily closely by F i that do satisfy the assumptions.…”

Section: Subjective Hqrementioning

confidence: 99%

Heterogeneous quantal response equilibrium and cognitive hierarchies

Rogers

Palfrey

Camerer

2009

Journal of Economic Theory

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164

103

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We explore an equilibrium model of games where players' choice behavior is given by logit response functions, but their payoff responsiveness is heterogeneous. We extend the definition of quantal response equilibrium to this setting, calling it heterogeneous quantal response equilibrium (HQRE), and prove existence under weak conditions. We generalize HQRE to allow for limited insight, in which players can only imagine others with low responsiveness. We identify a formal connection between this new equilibrium concept, called truncated quantal response equilibrium (TQRE), and the Cognitive Hierarchy (CH) model. We show that CH can be approximated arbitrarily closely by TQRE. We report a series of experiments comparing the performance of QRE, HQRE, TQRE and CH. A surprise is that the fit of the models are quite close across a variety of matrix and dominance-solvable asymmetric information betting games. The key link is that in the QRE approaches, strategies with higher expected payoffs are chosen more often than strategies with lower expected payoff. In CH this property is not built into the model, but generally holds true in the experimental data.JEL classification numbers: 024, 026

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Section: Subjective Hqrementioning

confidence: 99%

Heterogeneous quantal response equilibrium and cognitive hierarchies

Rogers

Palfrey

Camerer

2009

Journal of Economic Theory

Self Cite

164

103

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“…We found no such references to Bayesian statistics in EE in all periods, except, as discussed above, in Smith (1964). Bayesian approaches are sometimes applied in EE to optimize experimental designs , (e.g., El-Gamal et al 1993;El-Gamal and Palfrey 1996;Kessels et al 2011 or in structural modeling to find the model best fitting the data (e.g. Cipriani et al, 2012), but Bayesian statistics in both cases are not used to discuss experimental results nor to assess the validity of hypotheses in the way above mentioned the studies mentioned above is quoted in a significant manner in the EE literature 14 .…”

Section: The Birth Of a Long-standing Statistical Controversy In Psycmentioning

confidence: 86%

Estimating Rationality in Economics: A History of Statistical Methods in Experimental Economics

Vallois

Jullien

2018

SSRN Journal

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Abstract.Experimental economists increasingly apply econometric techniques to interpret their data, as suggests the emergence of "experimetrics" in the 2000s. Yet statistics remains a minor topic in historical and methodological writings on experimental economics (EE). This article aims to address this lacuna .To do so, we analyze the use of statistical tools in EE from early economics experiments of the 1940s-1950s to the present days. Our narrative is based on qualitative analysis of papers published in early periods and quantitative analysis of papers published in more recent periods. Our results reveal a significant change in EE' statistical methods, namely an evolution from purely descriptive methods to more sophisticated and standardized techniques. We also highlight that, despite the decisive role played by statistics in the way EE estimate the rationality of individuals or markets, statistics are still considered as involving non-methodological issues, i.e., as involving only purely technical issues. Our historical analysis shows that this technical conception was the result of a longrun evolution of the process of scientific legitimization of EE, which allowed experimental economists to escape from psychologist's more reflexive culture toward statistics.

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“…In fact some of the findings here are probably true for a very \vide class of experimental games. For example, the estimate of a > 0, reflecting learning by-doing, was also recovered in McKelvey and Palfrey (1992) and El-Gama! et al (1991), and is supported widely in informal data analysis of most game experiments.…”

Section: Discussionmentioning

confidence: 99%