Related papers: A Ladder Tournament
There is an innate human tendency, one might call it the "league table mentality," to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schr\"{o}dinger bridges we are able to…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
The career of an employee can be described (under certain circumstances) by a random walk, where the states of the random walk are determined by the level and position of an employee. At each decision moment the state of the employee is…
Ranks estimated from data are uncertain and this poses a challenge in many applications. However, estimated ranks are deterministic functions of estimated parameters, so the uncertainty in the ranks must be determined by the uncertainty in…
Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the…
The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract…
Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for…
We provide a self-contained introduction to finite extensive games with perfect information. In these games players proceed in turns having, at each stage, finitely many moves to their disposal, each play always ends, and in each play the…
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…
Chess is an emblematic sport that stands out because of its age, popularity and complexity. It has served to study human behavior from the perspective of a wide number of disciplines, from cognitive skills such as memory and learning, to…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices. This paper comprehensively analyzes games of rank one, and shows the following: (1) For a game of rank r, the set of its Nash equilibria is the…
As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here…
The demand for global university league tables has been high over the past two decades. However, significant criticism of their methodologies is accumulating without being addressed. I revisit global university league tables by normalizing…
We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to firms, and directed labeled edges correspond to debt contracts between them. The existence of cycles in…
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…
An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here we use a minimal mathematical model to explain this…
Ranking is used in sport leagues to determine a champion and/or to decide on promotion/relegation of teams. Arguably, the best known ranking method relies on scores obtained by cumulating the points associated with the wins and the draws of…