Related papers: Banach-Mazur game played in partially ordered sets
We study a game first introduced by Martin (actually we use a slight variation of this game) which plays a role for measure analogous to the Banach-Mazur game for category. We first present proofs for the basic connections between this game…
An infinite game on the set of real numbers appeared in Matthew Baker's work [Math. Mag. 80 (2007), no. 5, pp. 377--380] in which he asks whether it can help characterize countable subsets of the reals. This question is in a similar spirit…
The Banach-Mazur game, Schmidt's game and McMullen's absolute winning game are three quintessential intersection games. We investigate their determinacy on the real line when the target set for either player is a Bernstein set, a…
Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…
A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…
Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…
This paper deals with different concepts for characterizing the size of mathematical objects. A game theoretic investigation and generalization of two size concepts, which can both be formulated in topological terms, is provided: the so…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Two structures $A$ and $B$ are $n$-equivalent if player II has a winning strategy in the $n$-move Ehrenfeucht-Fra\"iss\'e game on $A$ and $B$. In earlier papers we studied $n$-equivalence classes of ordinals and coloured ordinals. In this…
The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi…
The article studies topological games that arise in the study of the continuity of operations in groups with topology, such as paratopological and semitopological groups. These games are modifications of the Banach--Mazur game. Given a…
Heifetz, Meier, and Schipper (2013) introduced dynamic game with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
The notion of Aronszajn-null sets generalizes the notion of Lebesgue measure zero on the real line and the Euclidean space to infinite dimensional Banach spaces. We present a game-theoretic approach to Aronszajn-null sets, establish its…
We prove that a player $\alpha$ has a winning strategy in the Banach--Mazur game on a space $X$ if and only if $X$ is F-Y countably $\pi$-domain representable. We show that Choquet complete spaces are F-Y countably domain representable. We…
We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be…
We extend Solovay's theorem about definable subsets of the Baire space to the generalized Baire space ${}^\lambda\lambda$, where $\lambda$ is an uncountable cardinal with $\lambda^{<\lambda}=\lambda$. In the first main theorem, we show that…
We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space…
It is known that the generalized Nash equilibrium problem can be reformulated as a quasivariational inequality. Our aim in this work is to introduce a variational approach to study the existence of solutions for generalized ordinal Nash…
The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is…