Related papers: Dutch Books and Combinatorial Games

Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property…

We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…

We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…

We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…

A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…

This thesis will be discussing scoring play combinatorial games and looking at the general structure of these games under different operators. I will also be looking at the Sprague-Grundy values for scoring play impartial games, and…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with…

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated…

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well…

Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…

This paper deals with N-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected…