Elicitation of expectations using Colonel Blotto

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.