Charles A. Holt’s research while affiliated with University of Virginia and other places

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Publications (244)


Belief elicitation
  • Chapter

February 2025

Charles A. Holt

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Angela M. Smith






Logit QRE a1 Attack Probability
Notes: The lines show the locus of QRE a1 attack frequencies as precision increases from left to right, with attack effectiveness reduced in equal absolute amounts from high (solid line) to low (dotted line).
Effects of Equal Absolute Increases in Attack Effectiveness
Notes: The mixed Nash equilibrium points (diamonds) are at intersections of sharp best‐response lines (straight or dotted). Quantal response equilibria (squares) are at intersections of the curved quantal response lines. The increase in attack effectiveness shifts the attacker quantal response line to the right, from dashed to dotted, which increases the predicted attack rate (square at lower right). The lower Nash equilibrium diamond for the dotted sharp best‐response line, in contrast, does not shift to the right.
Logit QRE a1 Proportions
Notes: The lines show the QRE locus of predicted a1 attack proportions as precision increases from left to right, with attack effectiveness reduced in equal proportions from high (solid line) to low (dotted line).
Effects of Equal Proportional Increases in A and B
Notes: The sharp lines are best responses, the curved solid lines are quantal responses for low attack effectiveness, and the curved dotted lines are quantal responses for high attack effectiveness. The quantal response equilibrium square shifts to the right (with higher predicted attack rates). In contrast, the Nash equilibrium at the intersection of the sharp dotted lines shifts to the left (with lower predicted attack rates).
Average a1 Attack Frequencies, ᾱ, by Round, with Equal Absolute Changes
Notes: The dashed lines connect data average dots for the LowAb treatment, and the solid lines connect data average dots for the High treatment. The Nash equilibrium prediction is represented by the flat line at 0.33 for both treatments. Data averages conform to Nash predictions in the LowAb treatment but are significantly higher High attack effectiveness treatment.

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Bilateral Conflict: An Experimental Study of Strategic Effectiveness and Equilibrium
  • Article
  • Publisher preview available

August 2023

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10 Reads

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2 Citations

Bilateral conflict involves an attacker with several alternative attack methods and a defender who can take various actions to better respond to different types of attack. These situations have wide applicability to political, legal, and economic disputes, but they are particularly challenging to study empirically because the payoffs are unknown. Moreover, each party has an incentive to behave unpredictably, so theoretical predictions are stochastic. This article reports results of an experiment where the details of the environment are tightly controlled. The results sharply contradict the Nash equilibrium predictions about how the two parties’ choice frequencies change in response to the relative effectiveness of alternative attack strategies. In contrast, nonparametric quantal response equilibrium predictions match the observed treatment effects. Estimation of the experimentally controlled payoff parameters across treatments accurately recovers the true values of those parameters with the logit quantal response equilibrium model but not with the Nash equilibrium model.

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Permutation tests for experimental data

April 2023

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136 Reads

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32 Citations

Experimental Economics

Unlabelled: This article surveys the use of nonparametric permutation tests for analyzing experimental data. The permutation approach, which involves randomizing or permuting features of the observed data, is a flexible way to draw statistical inferences in common experimental settings. It is particularly valuable when few independent observations are available, a frequent occurrence in controlled experiments in economics and other social sciences. The permutation method constitutes a comprehensive approach to statistical inference. In two-treatment testing, permutation concepts underlie popular rank-based tests, like the Wilcoxon and Mann-Whitney tests. But permutation reasoning is not limited to ordinal contexts. Analogous tests can be constructed from the permutation of measured observations-as opposed to rank-transformed observations-and we argue that these tests should often be preferred. Permutation tests can also be used with multiple treatments, with ordered hypothesized effects, and with complex data-structures, such as hypothesis testing in the presence of nuisance variables. Drawing examples from the experimental economics literature, we illustrate how permutation testing solves common challenges. Our aim is to help experimenters move beyond the handful of overused tests in play today and to instead see permutation testing as a flexible framework for statistical inference. Supplementary information: The online version contains supplementary material available at 10.1007/s10683-023-09799-6.


Endogenous reference price auctions for a diverse set of commodities: an experimental analysis

March 2023

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2 Reads

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1 Citation

Experimental Economics

Unlabelled: This paper is concerned with multi-object, multi-unit auctions with a budget constrained auctioneer who has noisy value estimates for each object. We propose a new allocation mechanism, the endogenous reference price auction, with two key features. First, bids are normalized across objects using "reference prices." Second, reference prices are set endogenously using information extracted from the bids submitted. We report on an experiment showing that a simple endogenous process mitigates value inaccuracies and improves three performance measures: the seller's profit, allocative efficiency and total surplus. These results have important implications for large auctions used in practice. Supplementary information: The online version contains supplementary material available at 10.1007/s10683-022-09783-6.



Citations (73)


... This intuition is incorrect. To illustrate, consider an experiment reported by Holt and Smith (2022) in which subjects competed for a fixed monetary prize by expending lab dollars on "effort" that has a specified cost per unit. One treatment contrast compared average total expenditures on "rent-seeking" activity with low effort cost (77, 83, 130, 81) against expenditures with high effort cost (132, 111, 93, 87). ...

Reference:

Permutation tests for experimental data
Rent Dissipation and Streamlined Costs: Laboratory Experiments
  • Citing Article
  • November 2023

Games and Economic Behavior

... By contrast, we do not take QRE as a starting point, and instead axiomatize solution concepts rather than response functions. Furthermore, our results differ in that they pin down the one-parameter class of logit QRE in particular, providing a novel justification for a quantal response function that has been widely used to analyze empirical data (see, e.g., Goeree, Holt, and Palfrey, 2016;Wright and Leyton-Brown, 2017;Goeree, Holt, and Palfrey, 2020). ...

Stochastic game theory for social science: a primer on quantal response equilibrium
  • Citing Chapter
  • October 2020

... Old theories attributed labor market gaps to discrimination (Anderson et al., 2006;Riach & Rich, 2010;Blau & Kahn, 2017;Neumark, 2018). Nowadays, even if we can attribute these disparities in part to social prejudices, more recent researches argue that the structure and the framework of the labor market make equal opportunities in the workplace difficult to attend between the two genders. ...

Discrimination: Experimental Evidence from Psychology and Economics
  • Citing Chapter
  • March 2006

... The permutation test in imcRtools (version 1.0.2) [32] was employed to determine whether there was a statistically significant interactions/avoidances between each cell type within each CN in comparison with that of random observations. Permutation test is a nonparametric statistical method based on data rearrangement (permutation) that is used to test the null hypothesis in a hypothesis test [33]. It does not depend on the distribution assumptions of the data and can be used for various statistics and complex experimental designs. ...

Permutation tests for experimental data

Experimental Economics

... This framework is closely related to the one he introduced to study affiliated private value auctions (Kagel et al., 1987). Now, more than 35 years later, that same structure is used in the paper by Armantier and Holt (2023) where they study auction mechanisms for world relevant applications: multi-object, multi-unit auctions, with a budget-constrained auctioneer who is uncertain of the values of the objects. The main insight is that the auctioneer can improve outcomes by incorporating information contained in submitted bids when setting reference prices. ...

Endogenous reference price auctions for a diverse set of commodities: an experimental analysis
  • Citing Article
  • March 2023

Experimental Economics

... Behavioral biases can be analyzed by gender, according to Hand (2020) research on gender and environmental concern reveals that women tend to have higher levels of environmental concern than men Davidson and Freudenburg (1996); Xiao and Hong (2018) ;Hunter, Hatch and Johnson (2004). Although several possible hypotheses have suggested explaining this difference, only one, the risk issues, has received consistent support Davis and Holt (1993b) 3 and Friedl, Neyse and Schmidt (2018). ...

Experimental Economics
  • Citing Book
  • July 2021

... Moreover, experimental research on bargaining games (Brosig, Weimann, and Yang 2003;Holt and Sieberg 2022), ultimatum games (Costa-Gomes et al. 2019), trust games (Burks, Carpenter, and Verhoogen 2003), dictator games (Diekmann 2004), redistribution and public goods games (Buso et al. 2021;Cassar and Klein 2019;Lange, Schmitz, and Schwirplies 2022) documents that experiencing the other players' position, i.e., role-reversal, may affect outcomes and behavior through time, increasing trust, cooperation, and pro-social choices. 1 For example, among others, Burks, Carpenter, and Verhoogen (2003) compare a single-role versus role switching trust game, and find that trust and reciprocity are both affected by a switch in the parties' roles, and Costa-Gomes et al. (2019) compare the strategy method and sequential strategies in an ultimatum game, and find that in a sequential game, participants are significantly more likely to treat others how they would like to be treated. Most recently, Solomon (2022) analyzes how role-switching between a plaintiff and a defendant affects learning in a signaling game of pretrial bargaining, and finds that switching roles facilitate learning by allowing individuals to become more familiar with the role of their opponent. ...

Bargaining, Fairness and Conflict

Homo Oeconomicus

... The contribution in this paper is to provide new insights on the waterbed effect under realworld carbon-market designs, and connect it to basic economic principles on pass-through from the classic literature on tax incidence (Jenkin, 1872;Weyl and Fabinger, 2013). Our modelling spans market designs that adjust the emissions cap based on allowance prices (including price ceilings and floors) (Roberts and Spence, 1976;Pizer, 2002;Newell et al., 2005;Borenstein et al., 2019;Karp and Traeger, 2024;Burtraw et al., 2022) and those, as in the EU, that respond to changes in the quantity of allowances in circulation (Perino, 2018;Gerlagh et al., 2021). In these carbon markets, the waterbed effect typically takes on intermediate values between zero and 100%, thus enabling overlapping policies to affect aggregate emissions. ...

Price-Responsive Allowance Supply in Emissions Markets
  • Citing Article
  • May 2022

Journal of the Association of Environmental and Resource Economists

... The fact that agents play games against their neighboring agents brings up an immediate tension between the individual selfinterests of agents playing the local game and the promoting of a common good, like an efficient global solution to the game [4,5]. Common examples of these multi-agent scenarios include voting, crime reporting, and crowdfunding [6,7]. A similar situation also occurs in Boolean games, where each player tries to satisfy its individual goal [4,8,9]. ...

An Experimental Study of Strategic Voting and Accuracy of Verdicts with Sequential and Simultaneous Voting