Related papers: Optimal Strategies and Rules for the Game of Horse
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…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of…
Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…
Classical voting rules assume that ballots are complete preference orders over candidates. However, when the number of candidates is large enough, it is too costly to ask the voters to rank all candidates. We suggest to fix a rank k, to ask…
The subject of this paper is a variation of a blackjack game, mainly popular in some parts of Europe where it is known as einz (in German slang: one). We describe the rules of this game, indicate its main characteristics, give some…
We give examples of situations -- stochastic production, military tactics, corporate merger -- where it is beneficial to concentrate risk rather than to diversify it, that is, to put all eggs in one basket. Our examples admit a dual…
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…
This paper studies Ebert's hat problem with four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies…
The maximum surveillance of a target which is holding course is considered, wherein an observer vehicle aims to maximize the time that a faster target remains within a fixed-range of the observer. This entails two coupled phases: an…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
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…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…
This paper illustrates how a 3 degrees of freedom, Cartesian robot can be given the task of playing ping pong against a human player. We present an algorithm based on particle swarm optimization for the robot to calculate when and how to…
Within college basketball, the decision to foul or not with a 3-point lead (the "foul up 3" dilemma) significantly impacts teams. A single fouling decision can directly determine the outcome of a game or even an entire season. Within this…
This is an attempt to formalize the conditions of possibility for free, libre, open access to scientific knowledge within a game. The challenge is to enunciate the terms under which agents participating in the Grand conversation of science…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…
There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion…