A Colonel Blotto Gladiator Game

References

• Abbe E, Huang S-L, Telatar E. Proof of the outage probability conjecture for MISO channels. (2011) . ArXiv ePrint 1103.5478 March 28, http://arxiv.org/abs/1103.5478Google Scholar
• Adamo T, Matros A. A Blotto game with incomplete information. Econom. Lett. (2009) 105(1):100–102Crossref, Google Scholar
• Alcalde J, Dahm M. Rent seeking and rent dissipation: A neutrality result. J. Public Econom. (2010) 94(1–2):1–7Crossref, Google Scholar
• Arad A. The tennis coach problem: A game-theoretic and experimental study. The B.E.J. Theoret. Econom. (2009) 12(1). Article 10. doi:10.1515/1935-1704.1738Google Scholar
• Bellman R. On “Colonel Blotto” and analogous games. SIAM Rev. (1969) 11(1):66–68Crossref, Google Scholar
• Blackett DW. Some Blotto games. Naval Res. Logist. Quart. (1954) 1(1):55–60Crossref, Google Scholar
• Blackett DW. Pure strategy solutions of Blotto games. Naval Res. Logist. Quart. (1958) 5(2):107–109Crossref, Google Scholar
• Bock ME, Diaconis P, Huffer FW, Perlman MD. Inequalities for linear combinations of gamma random variables. Canada J. Statist. (1987) 15(4):387–395Crossref, Google Scholar
• Borel É. La théorie des jeux et les équations intégrales à noyau symétrique. C. R. Acad. Sci. Paris (1921) 173(25):1304–1308Google Scholar
• Borel E. The theory of play and integral equations with skew symmetric kernels. Econometrica (1953) 21(1):97–100Crossref, Google Scholar
• Borel E, Ville J. Application de la Théorie des Probabilités aux Jeux de Hasard. Gauthier-Villars (1938) . Reprinted in Borel E, Chéron A (1991). Théorie Mathématique du Bridge à la Portée de Tous, (Editions Jacques Gabay, Paris)Google Scholar
• Chowdhury SM, Kovenock D, Sheremeta RM. An experimental investigation of Colonel Blotto games. Econom. Theory. (2010) . ForthcomingGoogle Scholar
• Cook JD. Numerical computation of stochastic inequality probabilities. (2008) . Tech. Rep. 46, UT MD Anderson Cancer Center Department of Biostatistics, Houston, TXGoogle Scholar
• Cook JD, Nadarajah S. Stochastic inequality probabilities for adaptively randomized clinical trials. Biom. J. (2006) 48(3):356–365Crossref, Google Scholar
• Cooper JN, Restrepo RA. Some problems of attack and defense. SIAM Rev. (1967) 9(4):680–691Crossref, Google Scholar
• Corchón L. The theory of contests: A survey. Rev. Econom. Design (2007) 11(2):69–100Crossref, Google Scholar
• Corchón L, Dahm M. Foundations for contest success functions. Econom. Theory (2010) 43(1):81–98Crossref, Google Scholar
• De Schuymer B, De Meyer H, De Baets B. Optimal strategies for equal-sum dice games. Discrete Appl. Math. (2006) 154(18):2565–2576Crossref, Google Scholar
• Diaconis P, Miclo L. On times to quasi-stationarity for birth and death processes. J. Theoret. Probab. (2009) 22(3):558–586Crossref, Google Scholar
• Diaconis P, Perlman MD, Block HW, Sampson AR, Savits TH. Bounds for tail probabilities of weighted sums of independent gamma random variables. Topics in Statistical Dependence (Somerset, PA, 1987) (1990) (Inst. Math. Statist., Hayward, CA) 147–166IMS Lecture Notes Monogr. Ser., Vol. 16Crossref, Google Scholar
• Fréchet M. Commentary on the three notes of Emile Borel. Econometrica (1953a) 21(1):118–124Crossref, Google Scholar
• Fréchet M. Emile Borel, initiator of the theory of psychological games and its application. Econometrica (1953b) 21(1):95–96Crossref, Google Scholar
• Friedman L. Game-theory models in the allocation of advertising expenditures. Oper. Res. (1958) 6(5):699–709Link, Google Scholar
• Garfinkel MR, Skaperdas S, Sandler T, Hartley K. Economics of conflict: An overview. Handbook of Defense Economics, Handbook of Defense Economics (2007) 2(Elsevier, Amsterdam) 649–709Chap. 22Crossref, Google Scholar
• Golman R, Page S. General Blotto: Games of allocative strategic mismatch. Public Choice (2009) 138(3–4):279–299Crossref, Google Scholar
• Groeneveld RA, Meeden G. The mode, median, and mean inequality. Amer. Statist. (1977) 31(3):120–121Google Scholar
• Gross O, Wagner R. A continuous Colonel Blotto game. (1950) . Tech. Rep. RM-408, RAND Corporation, Santa Monica, CAGoogle Scholar
• Gross OA. The symmetric Blotto game. (1950) . Tech. Rep. RM-424, RAND Corporation, Santa Monica, CAGoogle Scholar
• Hart S. Discrete Colonel Blotto and General Lotto games. Internat. J. Game Theory (2008) 36(3–4):441–460Crossref, Google Scholar
• Heuer GA. Three-part partition games on rectangles. Theoret. Comput. Sci. (2001) 259(1–2):639–661Crossref, Google Scholar
• Hirshleifer J. Conflict and rent-seeking success functions: Ratio vs. difference models of relative success. Public Choice (1989) 63(2):101–112Crossref, Google Scholar
• Ibragimov IA. On the composition of unimodal distributions. Theory Probab. Appl. (1956) 1(2):255–260Crossref, Google Scholar
• Jorswieck EA, Boche H. Behavior of outage probability in MISO systems with no channel state information at the transmitter. Information Theory Workshop, 2003. Proceedings. 2003 IEEE. (2003) (IEEE, Piscataway, NJ) 353–356Crossref, Google Scholar
• Kaminsky KS, Luks EM, Nelson PI. Strategy, nontransitive dominance and the exponential distribution. Austral. J. Statist. (1984) 26(2):111–118Crossref, Google Scholar
• Karlin S. Total Positivity (1968) I(Stanford University Press, Stanford, CA) Google Scholar
• Konrad KA. Strategy and Dynamics in Contests (2009) (Oxford University Press, Oxford, UK) Crossref, Google Scholar
• Kovenock D, Roberson B, Garfinkel MR, Skaperdas S. Conflicts with multiple battlefields. (2010) (Oxford University Press, Oxford, UK) Oxford Handbook of the Economics of Peace and ConflictsGoogle Scholar
• Kvasov D. Contests with limited resources. J. Econom. Theory (2007) 136(1):738–748Crossref, Google Scholar
• Lauritzen SL. Exchangeable Rasch matrices. Rend. Mat. Appl. (7) (2008) 28(1):83–95Google Scholar
• Lippman SA, McCardle KF. Dropout behavior in R&D races with learning. RAND J. Econ. (1987) 18(2):287–295Crossref, Google Scholar
• Olver FWJ, Lozier DW, Boisvert RF, Clark CW . NIST Handbook of Mathematical Functions (2010) (U.S. Department of Commerce National Institute of Standards and Technology, Washington, DC) Google Scholar
• Osborne MJ, Rubinstein A. A Course in Game Theory (1994) (MIT Press, Cambridge, MA) Google Scholar
• Penn AI. A generalized Lagrange-multiplier method for constrained matrix games. Oper. Res. (1971) 19(4):933–945Link, Google Scholar
• Powell R. Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack. Games Econom. Behav. (2009) 67(2):611–615Crossref, Google Scholar
• Rasch G. Probabilistic Models for Some Intelligence and Attainment Tests (1980) (The University of Chicago Press, Copenhagen) . Expanded version of the 1960 edition published by Danish Institute for Educational ResearchGoogle Scholar
• Roberson B. The Colonel Blotto game. Econom. Theory (2006) 29(1):1–24Crossref, Google Scholar
• Robson A. Multi-item contests. (2005) . ANUCBE School of Economics Working Papers 2005-446, Australian National University, College of Business and Economics, School of Economics. http://ideas.repec.org/p/acb/cbeeco/2005-446.htmlGoogle Scholar
• Sahuguet N, Persico N. Campaign spending regulation in a model of redistributive politics. Econom. Theory (2006) 28(1):95–124Crossref, Google Scholar
• Shubik M, Weber RJ. Systems defense games: Colonel Blotto, command and control. Naval Res. Logist. Quart. (1981) 28(2):281–287Crossref, Google Scholar
• Sion M, Wolfe P. On a game without a value. Contributions to the Theory of Games (1957) 3(Princeton University Press, Princeton, NJ) Annals of Mathematics StudiesGoogle Scholar
• Skaperdas S. Contest success functions. Econom. Theory (1996) 7(2):283–290Crossref, Google Scholar
• Székely GJ, Bakirov NK. Extremal probabilities for Gaussian quadratic forms. Probab. Theory Related Fields (2003) 126(2):184–202Crossref, Google Scholar
• Szymanski S. The economic design of sporting contests. J. Econom. Lit. (2003) 41(4):1137–1187Crossref, Google Scholar
• Tang P, Shoham Y, Lin F. Designing competitions between teams of individuals. Artificial Intelligence (2010) 174(11):749–766Crossref, Google Scholar
• Telatar E. Capacity of multi-antenna Gaussian channels. Eur. Trans. Telecommunications (1999) 10(6):585–595Crossref, Google Scholar
• Tukey JW. A problem in strategy. Econometrica (1949) 17(1):73Google Scholar
• Tullock G, Buchanan JM, Tollison RD, Tullock G. Efficient rent-seeking. Towards a Theory of the Rent-Seeking Society (1980) (Texas A&M University Press, College Station, Texas) 97–112Google Scholar
• von Neumann J. Communication on the Borel notes. Econometrica (1953) 21(1):124–127Crossref, Google Scholar
• Weinstein J. Two notes on the Blotto game. The B.E.J. Theoret. Econom. (2012) 12(1). Article 7. doi:10.1515/1935-1704.1893Google Scholar
• Yu Y. On an inequality of Karlin and Rinott concerning weighted sums of i.i.d. random variables. Adv. in Appl. Probab. (2008) 40(4):1223–1226Crossref, Google Scholar
• Yu Y. Some stochastic inequalities for weighted sums. Bernoulli (2011) 17(3):1044–1053Crossref, Google Scholar