Related papers: Baire spaces and infinite games

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…

We prove that every repeated game with countably many players, finite action sets, and tail-measurable payoffs admits an $\epsilon$-equilibrium, for every $\epsilon > 0$.

It was shown in Flesch and Solan (2022) with a rather involved proof that all two-player stochastic games with finite state and action spaces and shift-invariant payoffs admit an $\epsilon$-equilibrium, for every $\epsilon>0$. Their proof…

Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding different notions of bases in Banach spaces and lattices. For the…

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…

Hausdorff's paradoxical decomposition of a sphere with countably many points removed (the main precursor of the Banach-Tarski paradox) actually produced a partition of this set into three pieces A,B,C such that A is congruent to B (i.e.,…

We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because…

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…

We consider the degrees of non-computability (Weihrauch degrees) of finding winning strategies (or more generally, Nash equilibria) in infinite sequential games with certain winning sets (or more generally, outcome sets). In particular, we…

Bachet's game is a variant of the game of Nim. There are $n$ objects in one pile. Two players take turns to remove any positive number of objects not exceeding some fixed number $m$. The player who takes the last object loses. We consider a…

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to obtain the outcome, which player has a winning strategy, of a given combinatorial game. Positions of…

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive $C_{0}$-semigroups under the topology of uniform weak operator convergence on compact subsets of $\mathbb{R}_{+}$.…

Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…

We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.

We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: Consistently, there is a nowhere precipitous normal ideal $I$ on $\aleph_2$ such that player nonempty wins the pressing down game of…

We consider transferable utility cooperative games with infinitely many players and the core understood in the space of bounded additive set functions. We show that, if a game is bounded below, then its core is non-empty if and only if the…

Let $A$ be a unital Banach $\star$-algebra with unity $1$, $X$ be a Banach space and $\phi : A \times A \to X$ be a continuous bilinear map. We characterize the structure of $\phi$ where it satisfies any of the following properties: $$a,b…

In classical Monty Hall problem, one player can always win with probability 2/3. We generalize the problem to the quantum domain and show that a fair two-party zero-sum game can be carried out if the other player is permitted to adopt…

In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we…