Related papers: Baire spaces and infinite games

New results on the Baire product problem are presented. It is shown that an arbitrary product of almost locally ccc Baire spaces is Baire; moreover, the product of a Baire space and a 1st countable space which is $\beta$-unfavorable in the…

Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…

This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian games with nonatomic players, using direct information structures and obedient strategies. The main results demonstrate full implementation in a…

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…

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space of Baire functions is the Banakh-Gabriyelyan problem: Let $\alpha$ be a…

In this paper we present a few properties of $K$-partitions, which are partitions of Baire spaces such that all subfamilies of such a partition sum to a set with the Baire property. Among the result proven we have general existence result…

Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is…

Let f:X -> Y be an onto map between compact spaces such that all point-inverses of f are zero-dimensional. Let A be the set of all functions u:X -> I=[0,1] such that $u[f^\leftarrow(y)]$ is zero-dimensional for all y in Y. Do almost all…

We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach's contraction property. As an application, we demonstrate the existence of Nash equilibrium in a…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the…

In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called $\mathcal…

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…

We construct an appropriate metric on the collection of piecewise $\mathcal C^r$ maps defined on a compact interval. Although this metric space turns out to be not complete, we show that it is indeed a Baire space. As an application, we…

We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games…

In this paper we consider the question of distributional chaos on non-compact metric dynamical systems. We focus on a shift space over a countable alphabet, the Baire Space. We prove that on the Baire Space subshifts of finite type exhibit…

We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a…

We define $\Delta$-Baire spaces. If a paratopological group $G$ is $\Delta$-Baire space, then $G$ is a topological group. Locally pseudocompact spaces, Baire $p$-spaces, Baire $\Sigma$-spaces, products of \v{C}ech-complete spaces are…

This paper studies Bayesian games with general action spaces, correlated types and interdependent payoffs. We introduce the condition of ``decomposable coarser payoff-relevant information'', and show that this condition is both sufficient…

Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps in a metric space are…

The aim of this note is to investigate the open-open game of uncountable length. We introduce a cardinal number $\mu(X)$, which says how long the Player I has to play to ensure a victory. It is proved that $\su(X)\leq\mu(X)\leq\su(X)^+$. We…