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Elicitation of expectations using Colonel Blotto

Published online by Cambridge University Press:  14 March 2025

Ronald Peeters Open the ORCID record for Ronald Peeters [Opens in a new window]  and
Leonard Wolk
Ronald Peeters*
Affiliation:
Department of Economics, University of Otago, Dunedin, New Zealand
Leonard Wolk*
Affiliation:
Department of Finance, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
*
[email protected]
[email protected]
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Abstract

We develop a mechanism based on the Colonel Blotto game to elicit (subjective) expectations in a group-based manner. In this game, two players allocate resources over possible future events. A fixed prize is awarded based on the amounts the players allocate to the realized event. We consider two payoff variations: under the proportional-prize rule, the award is split proportionally to the resources that players allocate to the realized event; under the winner-takes-all rule, the full award is given to the player who allocate the most resources to the realized event. When probabilities by which events realize are common knowledge to the players, both games are Bayesian–Nash incentive compatible in the sense that (expected) equilibrium allocations perfectly reflect the true realization probabilities. By means of a laboratory experiment, we find that in a setting where realization probabilities are common knowledge the game with the proportional-prize rule (Prop) elicits better distributions compared to both the winner-takes-all variation (Win) and a benchmark mechanism based on an individual-based proper scoring rule (Ind). Without common knowledge of realization probabilities Prop is at least as good as Ind, showing that it is possible to use a game to elicit expectations in a similar fashion to using a proper scoring rule.

Keywords

Colonel BlottoExpectation elicitationExperimentBehavioral mechanism design

JEL classification

D84: Expectations • Speculations C92: Laboratory, Group Behavior D83: Search • Learning • Information and Knowledge • Communication • Belief • Unawareness C72: Noncooperative Games
Type
Original Paper
Information
Experimental Economics , Volume 22 , Issue 1 , 15 March 2019 , pp. 268 - 288
Copyright
Copyright © 2018 Economic Science Association

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10683-018-9596-x) contains supplementary material, which is available to authorized users.

We thank Matt Embrey, Glenn Harrison, Georgia Kosmopoulou, Carlos Lamarche, Josh Miller, Paulo Somaini, Martin Strobel, Alexander Westkamp, the editor, two anonymous referees, and the audiences at the CEREC Workshop in Economics (Brussels, 2015), the Conference on Auctions, Competition, Regulation, and Public Policy (Lancaster, 2015), the Behavioral and Experimental Economics Symposium (Maastricht, 2015), the Experimental Finance Conference (Tucson, 2016; Heidelberg, 2018), the Australasian meeting of the Econometric Society (Auckland, 2018), VU Amsterdam as well as UMass-Lowell for very helpful comments and suggestions.

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