Simple Tournament Research Articles

Cyclically simple tournaments

Cyclically simple tournaments

Coloring tournaments: From local to global

The chromatic number of a directed graph D is the minimum number of colors needed to color the vertices of D such that each color class of D induces an acyclic subdigraph. Thus, the chromatic number of a tournament T is the minimum number of transitive subtournaments which cover the vertex set of T. We show in this note that tournaments are significantly simpler than graphs with respect to coloring. Indeed, while undirected graphs can be altogether “locally simple” (every neighborhood is a stable set) and have large chromatic number, we show that locally simple tournaments are indeed simple. In particular, there is a function f such that if the out-neighborhood of every vertex in a tournament T has chromatic number at most c, then T has chromatic number at most f(c). This answers a question of Berger et al.

Self-selection in tournaments: The case of chess players

We consider a simple tournament model in which individuals auto-select into the contest on the basis of their commonly known strength levels, and privately observed strength-shocks (reflecting temporary deviations from observed levels). The model predicts that the participation rate should increase with the player's observed strength, and the total awarded prize amount. Furthermore, under certain conditions self-selection implies that participants with high observed strength levels have smaller expected strength-shocks than those with low levels. Consequently, the latter should play better than predicted and the former worse (given their observed strength). These predictions are confronted with data from a large and high-prize chess tournament held in the USA. This tournament is divided into different sections, with players being able to play in the section to which their current chess rating (observed strength) belongs. As predicted, we find that within each section the participation probability increases with chess rating and prize amounts, and players with a relatively low (resp. high) rating are indeed the ones who have a better (resp. worse) relative performance.

Selection in Tournaments: The Case of Chess Players

We consider a simple tournament model in which individuals auto-select into the contest on the basis of their commonly known strength levels, and privately observed strength-shocks (reflecting temporary deviations from observed levels). The model predicts that the participation rate should increase with the player’s observed strength, and the total awarded prize amount. Furthermore, under certain conditions self-selection implies that participants with high observed strength levels have smaller expected strength-shocks than those with low levels. Consequently, the latter should play better than predicted and the former worse (given their observed strength). These predictions are confronted with data from a large chess tournament held in the USA. This tournament is divided into different sections, with players being able to play in the section to which their current chess rating (observed strength) belongs. As predicted, we find that within each section the participation probability increases with chess rating and prize amounts, and players with a relatively low (resp. high) rating are indeed the ones who have a better (resp. worse) relative performance.

Why Was It Europeans Who Conquered the World?

By the 1700s Europeans dominated the gunpowder technology, which was surprising, because it had originated in China and been used with expertise throughout Eurasia. To account for their dominance, historians have invoked competition, but it cannot explain why they pushed this technology further than anyone else. The answer lies with a simple tournament model of military competition that allows for learning by doing. Political incentives and military conditions then explain why the rest of Eurasia fell behind Europeans in developing the gunpowder technology. The consequences were huge, from colonialism to the slave trade and even the Industrial Revolution.

On the functional completeness of simple tournaments

The theory of multitraces provides a new proof that any simple tournament with more than two elements is functionally complete.

The operad of finite labeled tournaments

We study the operad of finite labeled tournaments. We describe the structure of suboperads of this operad generated by simple tournaments. We prove that a suboperad generated by a tournament with two vertices (i.e., the operad of finite linearly ordered sets) is isomorphic to the operad of symmetric groups, and a suboperad generated by a simple tournament with more that two vertices is isomorphic to the quotient operad of the free operad with respect to a certain congruence. We obtain this congruence explicitly.

Individual Transitions from Temporary to Permanent Job: What Consequences about Wage Diffences in France?

The paper investigates individual transitions from a temporary job (CDD) to a permanent job (CDI) in France. We present the transition from a temporary job to a permanent one as a simple tournament mechanism where promotion to CDI is based on a productivity norm. The equilibrium properties of the model show that wages differences between temporary jobs and permanent ones are positively correlated with uncertainty during tournament. This particular property is tested on the French Labour Survey 1990-2002, using an endogenous switching wage model to control for the contract type selection rule. A Neuman-Oaxaca decomposition method is used to identify the relative contribution of observables and unobservables in wage differentials. Using firm size as a proxy for uncertainty we compare the differential wage decomposition between large firm tournament and small firm tournament. Our results show that, in small firms, the characteristics which contribute to the selection tend to reduce the wage dispersion between CDI and CDD by 9,3%. These results do not reject the equilibrium property of the model according to which more uncertainty during tournament reduces players' incentives and would be compensated by an increased wage gap between promoted and not promoted.

Constructions Over Tournaments

We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.

Tournament Rewards and Risk Taking

I consider two seemingly unrelated puzzles. 1.Why is relative performance evaluation (RPE) used less in CEO compensation than agency theory suggests? 2.Why is sometimes, e.g., for fund managers, a 'modest' performance more highly rewarded than 'very high' performances? I consider a simple tournament model where agents can influence the spread of output in addition to its mean. I show that standard tournament rewards induce risky and lazy behavior from the agents. This finding sheds light on Puzzle 1. Second, I consider a scheme that ranks agents according to their relative closeness to a benchmark k. I show that there exists intermediate values of k such that the risky-lazy problem of the standard tournament can be mitigated, and first best level of effort can be implemented. This result sheds light on Puzzle 2.

Simple tournaments and sharply transitive groups

We prove that with the possible exception of total orders every tournament with sharply transitive group of automorphisms is simple.

Some remarks on simple tournaments

In this paper we shall prove some results about tournaments which we believe to be interesting both from an algebraic and a set theoretic point of view . The definition of a simple tournament, the subject of our title, was motivated by questions in algebra, but the results and the proofs we give are essentially set theoretical . We assume that the reader is familiar with the current notations of set theory . A tournament T = is a relational structure, where T is a non-empty set and -4 is a trichotomous binary relation on T, i .e . for every pair x, yET exactly one of the three relations

Embedding tournaments in simple tournaments

A tournament is simple if the corresponding relational system is simple in the algebraic sense. It is shown that any tournament T n with n nodes can be embedded in a simple tournament T n+1 apart from two exceptional types of tournaments which can be embedded in a simple tournament T n+2 .