Related papers: The generality of the zero-one laws

We consider discrete-time uncertain processes with finite state space and study the properties of game-theoretic upper expectations developed by Shafer and Vovk. We start by proving some basic properties, e.g. monotonicity, law of iterated…

A basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player" games, i.e., of Markov chains equipped with additive…

We show that the higher-order matching problem is decidable using a game-theoretic argument.

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…

We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…

We consider the Deduction Theorem used in the literature of game theory to run a purported proof by contradiction. In the context of game theory, it is stated that if we have a proof of $\phi \vdash \varphi$, then we also have a proof of…

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

The law of maturity is the belief that less-observed events are becoming mature and, therefore, more likely to occur in the future. Previous studies have shown that the assumption of infinite exchangeability contradicts the law of maturity.…

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…

The recent popularity of Wordle has revived interest in guessing games. We develop a general method for finding optimal strategies for guessing games while avoiding an exhaustive search. Our main contributions are several theorems that…

We study the joint laws of a continuous, uniformly integrable martingale, its maximum, and its minimum. In particular, we give explicit martingale inequalities which provide upper and lower bounds on the joint exit probabilities of a…

This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…

The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal."…

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game.…

We consider a finite state, finite action, zero-sum stochastic games with data defining the game lying in the ordered field of algebraic numbers. In both the discounted and the limiting average versions of these games we prove that the…

This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

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…