On Wednesday, September 16 the all-Russian seminar "Mathematical methods of decision analysis in economics, finance and politics" was held.
Speaker: Alexander Karpov (Heidelberg University, Germany; National Research University Higher School of Economics, Russia )
Title: A theory of knockout tournament seedings
This paper provides nested sets and vector representations of knockout tournaments seedings. The paper introduces classification of probability domain assumptions and a new set of axioms. Two new seeding methods are proposed: equal gap seeding and increasing competitive intensity seeding. Under different probability domain assumptions, several axiomatic justifications are obtained for equal gap seeding. A discrete optimization approach is developed. It is applied to justify equal gap seeding and increasing competitive intensity seeding. Some justification for standard seeding is obtained. Combinatorial properties of the seedings are studied.