Related papers: Kramnik vs Nakamura: A Chess Scandal
We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin and Alon et al. Fisher and Klimm…
We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for $n$-sided dice with pairwise ordering induced by the probability, relative to $1/2$, that a throw from one die is…
We consider a game played on an initially empty graph where two players alternate drawing an edge between vertices subject to the condition that no degree can exceed $k$. We show that for $k=3$, either player can avoid a Hamilton cycle, and…
A detailed analysis of matches played in the sport of Snooker during the period 1968-2020 is used to calculate a directed and weighted dominance network based upon the corresponding results. We consider a ranking procedure based upon the…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
The dishonest casino is a well-known hidden Markov model (HMM) often used in education to introduce HMMs and graphical models. A sequence of die rolls is observed with the casino switching between a fair and a loaded die. Instead of…
In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result - a…
Effects of a corrupt source on the dynamics of simultaneous move strategic games are analyzed both for classical and quantum settings. The corruption rate dependent changes in the payoffs and strategies of the players are observed. It is…
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
The most popular stability notion in games should be Nash equilibrium under the rationality of players who maximize their own payoff individually. In contrast, in many scenarios, players can be (partly) irrational with some unpredictable…
Cheating in chess, by using advice from powerful software, has become a major problem, reaching the highest levels. As opposed to the large majority of previous work, which concerned {\em detection} of cheating, here we try to evaluate the…
Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…
We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable…
There is a lot of statistical researches of Russian elections 04.12.2011. The purpose of this activity is to give a mathematical proof of large falsifications and to estimate possible 'real results of elections'. My purpose is to show that…
We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1…
A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…