Related papers: Scaling in Tournaments
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
In the classical leader election procedure all players toss coins independently and those who get tails leave the game, while those who get heads move to the next round where the procedure is repeated. We investigate a generalizion of this…
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
We consider two-person sports where each rally is initiated by a \emph{server}, the other player (the \emph{receiver}) becoming the server when he/she wins a rally. Historically, these sports used a scoring based on the \emph{side-out…
We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…
"The chance to win given a certain move" is an easily obtainable quantity from data and often quoted in gaming statistics. It is also the fundamental quantity that reinforcement learning AI bases on. Unfortunately, this conditional…
We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score,…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
In this paper, we explore the susceptibility of the independent Q-learning algorithms (a classical and widely used multi-agent reinforcement learning method) to strategic manipulation of sophisticated opponents in normal-form games played…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
The analysis of games and sports as complex systems can give insights into the dynamics of human competition, and has been proven useful in soccer, basketball, and other professional sports. In this paper we present a model for dodgeball, a…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among…
Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game…
Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
A co-evolutionary algorithm (CA) based chess player is presented. Implementation details of the algorithms, namely coding, population, variation operators are described. The alpha-beta or mini-max like behaviour of the player is achieved…
A variety of social, economic, and political interactions have long been modelled after Blotto games. In this paper, we introduce a general model of dynamic $n$-player Blotto contests. The players have asymmetric resources, and the…