相关论文: Merging of opinions in game-theoretic probability

This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…

Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by…

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…

When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

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.

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables…

Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which…

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the…

We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…

This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning…

Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of…

The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a…