Tournaments provide incentives through the prize spread. Agents are predicted to work harder for higher prize spreads, and thus principals are predicted to maximize the spread. This paper shows experimentally how changing institutional environments affect the way that principals structure tournament incentives, and the degree of wage compression. While in some settings tournaments provide power...

A collection of unlabelled tournaments P is called a hereditary property if it is closed under isomorphism and under taking induced sub-tournaments. The speed of P is the function n 7→ |Pn|, where Pn = {T ∈ P : |V (T )| = n}. In this paper, we prove that there is a jump in the possible speeds of a hereditary property of tournaments, from polynomial to exponential speed. Moreover, we determine t...

We analyze tournaments of heterogeneous players from an organizer’s perspective. Using a simple model of a noisy tournament, we demonstrate how the likelihood of selecting the best player, here termed the “predictive power” of a tournament, depends on the tournament format, the distribution of players’ types, and the overall noise level. We formalize the organizer’s decision problem for varying...

We consider the feedback vertex set and feedback arc set problems in bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We show that this result is the best we can attain when using a certain linear program as the lower bound on the optimal value. For the feedback arc set problem in bipartite tournaments, we show that a...

BACKGROUND/AIM To determine if Boys Bantam and Peewee and Girls U14 sustain fewer concussions, head hits, 'other injuries' and penalties in hockey tournaments governed by intensified fair play (IFP) than non-intensified fair play (NIFP). METHODS A prospective comparison of IFP, a behaviour modification programme that promotes sportsmanship, versus control (non-intensified, NIFP) effects on nu...

Given a tournament T and a positive integer k, the C3-Packing-T problem asks if there exists a least k (vertex-)disjoint directed 3-cycles in T . This is the dual problem in tournaments of the classical minimal feedback vertex set problem. Surprisingly C3-Packing-T did not receive a lot of attention in the literature. We show that it does not admit a PTAS unless P=NP, even if we restrict the co...

We disprove the following conjecture due to Vı́ctor Neumann-Lara: for every pair (r, s) of integers such that r > s > 2, there is an infinite set of circulant tournaments T such that the dichromatic number and the cyclic triangle free disconnection of T are equal to r and s, respectively. Let Fr,s denote the set of circulant tournaments T with dc(T ) = r and − →ω 3 (T ) = s. We show that for eve...