Abstract
A class of integer-valued allocation games—“General Lotto games”—is introduced and solved. The results are then applied to analyze the classical discrete “Colonel Blotto games”; in particular, optimal strategies are obtained for all symmetric Colonel Blotto games.
Similar content being viewed by others
References
Avrahami J, Kareev Y (2005) Allocation of resources in a competitive environment. The Hebrew University of Jerusalem (mimeo)
Bell RM, Cover TM (1980) Competitive optimality of the logarithmic investment. Math Oper Res 5:161–166
Billingsley P (1986) Probability and measure, 2nd edn. Wiley, New York
Borel E (1921) La Théorie du Jeu et les Équations Intégrales à Noyau Symétrique. Comptes Rendus de l’Académie des Sciences 173, 1304–1308. Translated by Savage LJ, The theory of play and integral equations with skew symmetric kernels. Econometrica 21 (1953) 97–100
Dekel E, Jackson MO, Wolinsky A (2004) Vote buying. Tel Aviv University, California Institute of Technology, and Northwestern University (mimeo)
Groh C, Moldovanu B, Sela A, Sunde U (2003) Optimal seedings in elimination tournaments. University of Bonn, Ben-Gurion University, and IZA (mimeo)
Lizzeri A (1999) Budget deficit and redistributive politics. Rev Econ Stud 66:909–928
Myerson RB (1993) Incentives to cultivate minorities under alternative electoral systems. Am Polit Sci Rev 87:856–869
Robertson B (2006) The colonel blotto game. Econ Theory 29:1–24
Sahuguet N, Persico N (2006) Campaign spending regulation in a model of redistributive politics. Econ Theory 28:95–124
Shubik M (1982) Game theory in the social sciences. MIT Press, Cambridge
Tukey JW (1949) A problem of strategy. Econometrica 17:73
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated with great admiration to David Gale on his 85th birthday.
Research partially supported by a grant of the Israel Science Foundation. The author thanks Judith Avrahami and Yaakov Kareev for raising the problem, Abraham Neyman for useful suggestions, and Tom Ferguson, Benny Moldovanu, and Aner Sela for comments and discussions.
Rights and permissions
About this article
Cite this article
Hart, S. Discrete Colonel Blotto and General Lotto games. Int J Game Theory 36, 441–460 (2008). https://doi.org/10.1007/s00182-007-0099-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-007-0099-9