Displaying similar documents to “On β-favorability of the strong Choquet game”

Generalized Choquet spaces

Samuel Coskey, Philipp Schlicht (2016)

Fundamenta Mathematicae

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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...

A dichotomy on Schreier sets

Robert Judd (1999)

Studia Mathematica

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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 ∞ ⊆ ℕ such that S α ( M ) = m i : i ∈ E : E ∈ S α ⊆ ℱ , or there exist infinite M = ( m i ) i = 1 ∞ , N ⊆ ℕ such that ℱ [ N ] ( M ) = m i : i ∈ F : F ∈ ℱ a n d F ⊂ N ⊆ S α .

Existence of the value of fixed duration dynamical games

Piotr Borówko, Witold Rzymowski

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

Equilibrium analysis of distributed aggregative game with misinformation

Meng Yuan, Zhaoyang Cheng, Te Ma (2024)

Kybernetika

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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

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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 value based on marginal contributions for multi–alternative games with restricted coalitions

Satoshi Masuya, Masahiro Inuiguchi (2010)

Kybernetika

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This paper deals with cooperative games with n players and r alternatives which are called multi-alternative games. In the conventional multi-alternative games initiated by Bolger, each player can choose any alternative with equal possibilities. In actual social life, there exist situations in which players have some restrictions on their choice of alternatives. Considering such situations, we study restricted multi-alternative games. A value for a given game is proposed.

On the open-open game

Peg Daniels, Kenneth Kunen, Haoxuan Zhou (1994)

Fundamenta Mathematicae

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We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which...