Infinite Asymptotic Games and (*)-Embeddings of Banach Spaces

Georgios-Nektarios I. Karadakis

Displaying similar documents to “Infinite Asymptotic Games and (*)-Embeddings of Banach Spaces”

On β-favorability of the strong Choquet game

László Zsilinszky (2011)

Colloquium Mathematicae

Similarity:

In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty $W_{δ}$ -subspace which is of the first category in itself.

Generalized Choquet spaces

Samuel Coskey, Philipp Schlicht (2016)

Fundamenta Mathematicae

Similarity:

We introduce an analog to the notion of Polish space for spaces of weight ≤ κ, where κ is an uncountable regular cardinal such that $κ^{< κ} = κ$ . Specifically, we consider spaces in which player II has a winning strategy in a variant of the strong Choquet game which runs for κ many rounds. After discussing the basic theory of these games and spaces, we prove that there is a surjectively universal such space and that there are exactly $2^{κ}$ many such spaces up to homeomorphism. We also establish a Kuratowski-like...

Equilibrium analysis of distributed aggregative game with misinformation

Meng Yuan, Zhaoyang Cheng, Te Ma (2024)

Kybernetika

Similarity:

This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player’s deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt $ϵ$ -Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing...

Linear complementarity problems and bi-linear games

Gokulraj Sengodan, Chandrashekaran Arumugasamy (2020)

Applications of Mathematics

Similarity:

In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of $𝐙$ -transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type...

A dichotomy on Schreier sets

Robert Judd (1999)

Studia Mathematica

Similarity:

We show that the Schreier sets $S_{α} (α < ω_{1})$ have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite $M = {(m_{i})}_{i = 1}^{\infty} \subseteq ℕ$ such that $S_{α} (M) = m_{i} : i \in E : E \in S_{α} \subseteq ℱ$ , or there exist infinite $M = {(m_{i})}_{i = 1}^{\infty}, N \subseteq ℕ$ such that $ℱ [N] (M) = m_{i} : i \in F : F \in ℱ a n d F \subset N \subseteq S_{α}$ .

Existence of the value of fixed duration dynamical games

Piotr Borówko, Witold Rzymowski

Similarity:

CONTENTS1. Introduction.......................................................................................................52. Game................................................................................................................63. Approximation condition....................................................................................84. Differential games of Friedman’s type.............................................................13 4.1. Game without delay....................................................................................13 4.2....

Applications of limited information strategies in Menger's game

Steven Clontz (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize $σ$ -compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize $σ$ -compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between $σ$ -compact and Menger spaces.

On Telgársky's question concerning β-favorability of the strong Choquet game

László Zsilinszky (2013)

Colloquium Mathematicae

Similarity:

Answering a question of Telgársky in the negative, it is shown that there is a space which is β-favorable in the strong Choquet game, but all of its nonempty $W_{δ}$ -subspaces are of the second category in themselves.

Extenders for vector-valued functions

Iryna Banakh, Taras Banakh, Kaori Yamazaki (2009)

Studia Mathematica

Similarity:

Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender $u : C_{\infty} (A, Y) \to C_{\infty} (X, Y)$ , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained...

Bayesian Nash equilibrium seeking for multi-agent incomplete-information aggregative games

Hanzheng Zhang, Huashu Qin, Guanpu Chen (2023)

Kybernetika

Similarity:

In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of either Bayesian games or deterministic aggregative games. We handle the aggregation function to adapt to incomplete-information situations. Since the feasible strategies are infinite-dimensional functions and lie in a non-compact set, the continuity of types brings barriers to seeking equilibria. To this end, we discretize...

Determinacy of adversarial Gowers games

Christian Rosendal (2014)

Fundamenta Mathematicae

Similarity:

We prove a game-theoretic dichotomy for $G_{δ σ}$ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis’ proof of Σ⁰₃ determinacy.

An example of the game of Banach and Mazur

A. Zięba (1957)

Colloquium Mathematicae

Similarity:

Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions

Atsushi Moritani, Tetsuzo Tanino, Keiji Tatsumi (2006)

Kybernetika

Similarity:

Cooperative games are very useful in considering profit allocation among multiple decision makers who cooperate with each other. In order to deal with cooperative games in practical situations, however, we have to deal with two additional factors. One is some restrictions on coalitions. This first factor has been taken into consideration through feasibility of coalitions. The other is partial cooperation of players. In order to describe this second factor, we consider fuzzy coalitions...

Infinite games and chain conditions

Santi Spadaro (2016)

Fundamenta Mathematicae

Similarity:

We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the $G_{δ}$ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak...

On some topological games

Telgársky, R.

Similarity: