Related papers: Multi-Opponent James Functions
We design two mechanisms that ensure that the majority preferred option wins in all equilibria. The first one is a simultaneous game where agents choose other agents to cooperate with on top of the vote for an alternative, thus overcoming…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
Based on NFL game data we try to predict the outcome of a play in multiple different ways. An application of this is the following: by plugging in various play options one could determine the best play for a given situation in real time.…
The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in…
With the vast amount of data collected on football and the growth of computing abilities, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of…
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…
In competitive games, it is common to assign each player a real number rating signifying their skill level. A rating system is a procedure by which player ratings are adjusted upwards each time they win, or downwards each time they lose.…
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
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…
This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to…
The objective of the present study is to present a computational model of the motion of a single athlete in a team and to compare the resulting trajectory with experimental data obtained in the field during competitions by match analysis…
We investigate an algorithm that assigns to any game in normal form an approximating game that admits an ordinal potential function. Due to the properties of potential games, the algorithm equips every game with a surrogate reward structure…
We use the Minority Game and some of its variants to show how efficiency depends on learning in models of agents competing for limited resources. Exact results from statistical physics give a clear understanding of the phenomenology, and…
Intuitively, experience playing against one mixture of opponents in a given domain should be relevant for a different mixture in the same domain. We propose a transfer learning method, Q-Mixing, that starts by learning Q-values against each…
Tennis is so popular that coaches and players are curious about factors other than skill, such as momentum. This article will try to define and quantify momentum, providing a basis for real-time analysis of tennis matches. Based on the…
In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's…
We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In constrast with previous MG, the best strategies are not always targeting the minority but are shifting…