Consider the following problem in game manipulation. A tournament designer who has full knowledge of the match outcomes between any possible pair of players would like to create a bracket for a balanced single-elimination tournament so that their favorite player will win. Although this problem has been studied in the areas of voting and tournament manipulation, it is still unknown whether it ca...

In this paper, we improve the best-known upper bound on the size of maximal tournament codes, and solve the related problem of edge-covering a complete graph with a minimum number of bipartite graphs of bounded size. Tournament codes are sets of {0,1,∗} strings closely related to self-synchronizing codes. We improve the current asymptotic upper bound on the size of a length-k tournament code (g...

Given a tournament score sequence s1 s2 } } } sn , we prove that there exists a tournament T on vertex set [1, 2, ..., n] such that the degree of any vertex i is si and the subtournaments of T on both the even and the odd vertices are transitive in the given order. This means that i beats j whenever i< j and i# j (mod 2). For any score sequence, we give an algorithm to construct a tournament of...

The (0, 1)-matrix A of order n is a tournament matrix provided A + A + I = J, where I is the identity matrix, and J = Jn is the all 1’s matrix of order n. It was shown by de Caen and Michael that the rank of a tournament matrix A of order n over a field of characteristic p satisfies rankp(A) ≥ (n − 1)/2 with equality if and only if n is odd and AA = O. This article shows that the rank of a tour...

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (i) we show that every stable choice function is generated by a unique simple choice function, which never excl...

We argue that financial analysts can be viewed as participants of two tournaments (the “All-star” tournament and the intrafirm tournament) and examine whether analysts are incentivized by the tournament compensation structure. Using data from 1991 to 2007, we find that interim losers are more likely to increase the boldness of their forecasts in the remainder of the tournament period than inter...

A basic result in Ramsey theory states that any tournament contains a “large” transitive subgraph. Since transitive tournaments contain only transitive subgraphs, it is natural to ask which subgraphs must appear in any large tournament that is “far” from being transitive. One result of this type was obtained by Fox and Sudakov who characterized the tournaments that appear in any tournament that...

A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an approximation algorithm with a constant approximation ratio. In addition, the proposed algorithm yields a solution that meets both the norepeater and mirrored co...

This paper analyses the relationship between workers’ gender and monetary incentives in an experimental setting based on a double-tournament scheme. The participants must choose between a piece-rate payment or a performance prize. The results show that women tend to shy away from competition, and are less sensitive than men to the monetary incentives of the tournament. In addition the tournamen...

Using Rado’s theorem for the existence of an independent transversal of family of subsets of a set on which a matroid is defined, we give a proof of Landau’s theorem for the existence of a tournament with a prescribed degree sequence. A similar approach is used to determine when a partial tournament can be extended to a tournament with a prescribed degree sequence. Mathematics Subject Classific...