Coalitional Colonel Blotto Games with Application to the Economics of Alliances

Authors


  • Dan Kovenock, University of Iowa, Department of Economics, Tippie College of Business, W284 PBB, 21 E. Market Street, Iowa City, IA 52242 (dan-kovenock@uiowa.edu). Brian Roberson, Purdue University, Department of Economics, Krannert School of Management, 403 W. State Street, West Lafayette, IN 47907 (brobers@purdue.edu).

  •  We have benefited from the helpful comments of Daniel G. Arce, Timothy Feddersen, Steven Slutsky, Konstantin Sonin, and participants in presentations at the Social Science Research Center Berlin (WZB), the 2006 Annual Meeting of the Midwest Political Science Association, the First World Meeting of the Public Choice Society, the Eighth Conference of the Society for the Advancement of Economic Theory, the 2007 Annual Meeting of the American Political Science Association, and the 2007 Annual Meeting of the Southern Economic Association. Part of this work was completed while Kovenock was Visiting Professor at the Social Science Research Center Berlin (WZB). Roberson acknowledges financial support from the Miami University Committee on Faculty Research and the Farmer School of Business. The authors, of course, remain solely responsible for any errors or omissions.

Abstract

In Borel’s Colonel Blotto game two players simultaneously allocate their respective endowments of a resource across n battlefields, the higher allocation wins each battlefield, and players maximize the number of battlefields won. Here we examine two players who may form an alliance before separately competing in two disjoint Colonel Blotto games against a common adversary. Despite a lack of common interests, unilateral transfers—in a direction consistent with the exploitation hypothesis—arise for a range of parameter configurations. Such transfers alter the adversary’s strategy and the combination of the direct and strategic effects benefits both allies.

Ancillary