Related papers: Banach-Mazur game played in partially ordered sets
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…
Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids. Huschenbett and the first author have shown how to…
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…
Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address…
We introduce two new model comparison games that characterize separability by first-order formulas with generalized quantifiers. One is built on the Ehrenfeucht-Fra\"iss\'e game and the other is a formula-size game.
To generalize complementarities for games, we introduce some conditions weaker than quasisupermodularity and the single crossing property. We prove that the Nash equilibria of a game satisfying these conditions form a nonempty complete…
We consider the following two-player game played on a separable, infinite-dimensional Banach space X. Player S chooses a positive integer k_1 and a finite-codimensional subspace X_1 of X. Then player P chooses x_1 in the unit sphere of X_1.…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…
We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a…
Mean-payoff games are important quantitative models for open reactive systems. They have been widely studied as games of full observation. In this paper we investigate the algorithmic properties of several sub-classes of mean-payoff games…
We prove that two natural definitions of residuality of families of F-sigma sets are equivalent. We make use of the Banach-Mazur game in the proof.
The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
Much progress has been made in misere game theory using the technique of restricted misere play, where games can be considered equivalent inside a restricted set of games without being equal in general. This paper provides a survey of…
Fragments of first-order logic over words can often be characterized in terms of finite monoids or finite semigroups. Usually these algebraic descriptions yield decidability of the question whether a given regular language is definable in a…
Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…
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 paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…