The Benefits of Fractionation in Competitive Resource Allocation
Tóm tắt
We leverage a new algorithm for numerically solving Colonel Blotto games to gain insight into a version of the game where players have different types of resources. Specifically, the winner of a battlefield is a function of a multi-dimensional allocation vector of each player. Our main focus is on the potential benefits of fractionation, which we define as the degree to which a player can quantize its resources. When players only have one type of resource, we show that the benefits to fractionation are in general, greatest in resource poor environments and against aggregated adversaries. We then extend the model to include random dropout and show that fractionation increases robustness to failure in resource poor environments but not resource rich environments. Finally, we show that when players have different types of resources, the benefits of fractionation are no longer mitigated by an increase in the total force size. Since many real-world resource allocation problems are multi-dimensional, our results illustrate the importance of analyzing multi-resource Blotto games in tandem with the traditional specification.
Tài liệu tham khảo
Arbatskaya, M., & Mialon, H. M. (2010). Multi-activity contests. Economic Theory, 43(1), 23–43.
Arbatskaya, M., & Mialon, H. M. (2012). Dynamic multi-activity contests. The Scandinavian Journal of Economics, 114(2), 520–538.
Behnezhad, S., Dehghani, S., Derakhshan, M., HajiAghayi, M., & Seddighin, S. (2017). Faster and simpler algorithm for optimal strategies of Blotto game. In Thirty-first AAAI conference on artificial intelligence.
Chien, S. F., Zarakovitis, C. C., Ni, Q., & Xiao, P. (2019). Stochastic asymmetric blotto game approach for wireless resource allocation strategies. IEEE Transactions on Wireless Communications, 18(12), 5511–5528.
Crutzen, B. S. Y., & Sahuguet, N. (2009). Redistributive politics with distortionary taxation. Journal of Economic Theory, 144(1), 264–279.
Ferdowsi, A., Sanjab, A., Saad, W., & Mandayam, N. B. (2017). Game theory for secure critical interdependent gas–power–water infrastructure. In 2017 Resilience week (RWS), (pp. 184–190). IEEE.
Friedman, L. (1958). Game-theory models in the allocation of advertising expenditures. Operations Research, 6(5), 699–709.
Golman, R., & Page, S. E. (2009). General blotto: Games of allocative strategic mismatch. Public Choice, 138(3–4), 279–299.
Gross, O., & Wagner, R. (1950). A continuous colonel blotto game. Technical report, Rand Project Air Force Santa Monica CA.
Hart, S. (2008). Discrete colonel blotto and general lotto games. International Journal of Game Theory, 36(3–4), 441–460.
Labib, M., Ha, S., Saad, W., & Reed, J. H. (2015). A colonel blotto game for anti-jamming in the internet of things. In 2015 IEEE global communications conference (GLOBECOM) (pp. 1–6). IEEE.
Min, M., Xiao, L., Xie, C., Hajimirsadeghi, M., & Mandayam, N. B. (2017). Defense against advanced persistent threats: A colonel blotto game approach. In 2017 IEEE international conference on communications (ICC) (pp. 1–6). IEEE.
Rinott, Y., Scarsini, M., & Yu, Y. (2012). A colonel Blotto gladiator game. Mathematics of Operations Research, 37(4), 574–590.
Roberson, B. (2006). The colonel blotto game. Economic Theory, 29(1), 1–24.
Roberson, B. (2010). Allocation games., Wiley encyclopedia of operations research and management science Hoboken: Wiley.
Roberson, B., & Kvasov, D. (2012). The non-constant-sum colonel blotto game. Economic Theory, 51(2), 397–433.
Shahrivar, E. M., & Sundaram, S. (2014). Multi-layer network formation via a colonel blotto game. In 2014 IEEE global conference on signal and information processing (GlobalSIP) (pp. 838–841). IEEE.
Snyder, J. M. (1989). Election goals and the allocation of campaign resources. Econometrica: Journal of the Econometric Society, 57, 637–660.
Thomas, C. (2018). N-dimensional blotto game with heterogeneous battlefield values. Economic Theory, 65(3), 509–544.
Schwartz, G., Loiseau, P., & Sastry, S. S. (2014). The heterogeneous colonel Blotto game. In 2014 7th international conference on NETwork Games, COntrol and OPtimization (NetGCoop) (pp. 232–238). IEEE.
Weinstein, J. (2012). Two notes on the Blotto game. The BE Journal of Theoretical Economics, 12(1), 1–13.