Majoritarian Blotto contests with asymmetric battlefields: an experiment on apex games

Montero, Maria; Possajennikov, Alex; Sefton, Martin; Turocy, Theodore L.

Abstract

We investigate a version of the classic Colonel Blotto game in which individual battlefields may have different values. Two players allocate a fixed discrete budget across battlefields. Each battlefield is won by the player who allocates the most to that battlefield. The player who wins the battlefields with highest total value receives a constant winner payoff, while the other player receives a constant loser payoff. We focus on apex games, in which there is one large and several small battlefields. A player wins if he wins the large and any one small battlefield, or all the small battlefields. For each of the games we study, we compute an equilibrium and we show that certain properties of equilibrium play are the same in any equilibrium. In particular, the expected share of the budget allocated to the large battlefield exceeds its value relative to the total value of all battlefields, and with a high probability (exceeding 90% in our treatments) resources are spread over more battlefields than are needed to win the game. In a laboratory experiment, we find that strategies that spread resources widely are played frequently, consistent with equilibrium predictions. In the treatment where the asymmetry between battlefields is strongest, we also find that the large battlefield receives on average more than a proportional share of resources. In a control treatment, all battlefields have the same value and our findings are consistent with previous experimental findings on Colonel Blotto games.

Citation

Montero, M., Possajennikov, A., Sefton, M., & Turocy, T. L. (2016). Majoritarian Blotto contests with asymmetric battlefields: an experiment on apex games. Economic Theory, 61(1), 55-89. https://doi.org/10.1007/s00199-015-0902-y

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2015
• Online Publication Date: Aug 12, 2015
• Publication Date: 2016-01
• Deposit Date: Aug 4, 2015
• Publicly Available Date: Sep 21, 2015
• Journal: Economic Theory
• Print ISSN: 0938-2259
• Electronic ISSN: 1432-0479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 61
• Issue: 1
• Pages: 55-89
• DOI: https://doi.org/10.1007/s00199-015-0902-y
• Keywords: Colonel Blotto, Contest theory, Majoritarian objective, Resource allocation, Experiment
• Public URL: https://nottingham-repository.worktribe.com/output/771212
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00199-015-0902-y
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00199-015-0902-y
• Contract Date: Aug 4, 2015