Related papers: Universal statistics of the knockout tournament
Ecologists and economists try to explain collective behavior in terms of competitive systems of selfish individuals with the ability to learn from the past. Statistical physicists have been investigating models which might contribute to the…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
How do different alliance mechanisms compare? In this work, we analyze various methods of forming an alliance in the Coalitional General Lotto game, a simple model of competitive resource allocation. In the game, Players 1 and 2…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
Despite growing interest in quantifying and modeling the scoring dynamics within professional sports games, relative little is known about what patterns or principles, if any, cut across different sports. Using a comprehensive data set of…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
This paper aims to explore the impact of tournament design on the incentives of the contestants. We develop a simulation framework to quantify the potential gain and loss from attacking based on changes in the probability of reaching the…
That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for…
Competitive balance is the subject of much interest in the sports analytics literature and beyond. In this paper, we develop a statistical network model based on an extension of the stochastic block model to assess the balance between teams…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
We derive an explicit formula for the probability of ruin of a gambler playing against an infinitely-rich adversary, when the games have payoff given by a general integer-valued probability distribution.
Competitive balance is an important concept for professional sports and one of the key issues that European football has to address in order to ensure its long-term prosperity. However, the quantification of competitive balance is not an…
Quitting games are one of the simplest stochastic games in which at any stage each player has only two possible actions, continue and quit. The game ends as soon as at least one player chooses to quit. The players then receive a payoff,…
The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about…
There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M. If M is an orthogonal matrix, then a digraph which supports M…
We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We…
Boxing has a long-standing problem with biased judging, impacting both professional and Olympic bouts. "Robberies", where boxers are widely seen as being denied rightful victories, threaten to drive fans and athletes away from the sport. To…