2021/06/01 by Dong Quan Vu, Vu, Dong Quan, Patrick Loiseau +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Voting Systems #Law, Economics, and Judicial Systems
paper · pdf · doi:10.48550/arxiv.2106.00617
openalex publication_date 2021/06/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We introduce the Colonel Blotto game with favoritism, an extension of the\nfamous Colonel Blotto game where the winner-determination rule is generalized\nto include pre-allocations and asymmetry of the players' resources\neffectiveness on each battlefield. Such favoritism is found in many classical\napplications of the Colonel Blotto game. We focus on the Nash equilibrium.\nFirst, we consider the closely related model of all-pay auctions with\nfavoritism and completely characterize its equilibrium. Based on this result,\nwe prove the existence of a set of optimal univariate distributions -- which\nserve as candidate marginals for an equilibrium -- of the Colonel Blotto game\nwith favoritism and show an explicit construction thereof. In several\nparticular cases, this directly leads to an equilibrium of the Colonel Blotto\ngame with favoritism. In other cases, we use these optimal univariate\ndistributions to derive an approximate equilibrium with well-controlled\napproximation error. Finally, we propose an algorithm -- based on the notion of\nwinding number in parametric curves -- to efficiently compute an approximation\nof the proposed optimal univariate distributions with arbitrarily small error.\n