2016/04/18 by Krishnendu Chatterjee, Chatterjee, Krishnendu, Rasmus Ibsen-Jensen +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Scheduling and Timetabling Solutions #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.1604.05090
openalex publication_date 2016/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning probability for a distinguished player, has received a lot of attention. Previous works consider the problem where the pairwise winning probabilities are known precisely, while we study how robust is the winning probability with respect to small errors in the pairwise winning probabilities. First, we present several illuminating examples to establish: (a)~there exist deterministic tournaments (where the pairwise winning probabilities are~0 or~1) where one optimal draw is much more robust than the other; and (b)~in general, there exist tournaments with slightly suboptimal draws that are more robust than all the optimal draws. The above examples motivate the study of the computational problem of robust draws that guarantee a specified winning probability. Second, we present a polynomial-time algorithm for approximating the robustness of a draw for sufficiently small errors in pairwise winning probabilities, and obtain that the stated computational problem is NP-complete. We also show that two natural cases of deterministic tournaments where the optimal draw could be computed in polynomial time also admit polynomial-time algorithms to compute robust optimal draws.