Related papers: Bayesian logistic betting strategy against probabi…
Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…
The game-theoretic version of Kolmogorov's strong law of large numbers says that Skeptic has a strategy forcing the statement of the law in a game of prediction involving Reality, Forecaster, and Skeptic. This note describes a simple…
We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…
We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game…
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe…
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital…
We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk \cite{sv}. In particular, concerning the rate of convergence of the strong…
Predicting the outcome of elections, sporting events, entertainment awards, and other competitions has long captured the human imagination. Such prediction is growing in sophistication in these areas, especially in the rapidly growing field…
Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have…
Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…
This note proposes a procedure for enhancing the quality of probabilistic prediction algorithms via betting against their predictions. It is inspired by the success of the conformal test martingales that have been developed recently.
We apply Game Theory to a mathematical representation of two competing teams of agents connected within a complex network, where the ability of each side to manoeuvre their resource and degrade that of the other depends on their ability to…
We analyze the dynamics of a forecasting game which exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of…
The online sports gambling industry employs teams of data analysts to build forecast models that turn the odds at sports games in their favour. While several betting strategies have been proposed to beat bookmakers, from expert prediction…
We study the computation of equilibria in prediction markets in perhaps the most fundamental special case with two players and three trading opportunities. To do so, we show equivalence of prediction market equilibria with those of a…