Related papers: On Ramsey properties, function spaces, and topolog…

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…

For a set-valued function $F$ on a compact subset $W$ of a manifold, spanning is a topological property that implies that $F(x) \ne 0$ for interior points $x$ of $W$. A myopic equilibrium applies when for each action there is a payoff whose…

We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…

The notion of "pseudocompactness" was introduced by Hewitt. The concept of relatively countably compact subspaces were explored by Marjanovic to show that a $\Psi$-space is pseudocompact. A topological space is said to be DRC (DRS) iff it…

This paper considers a special class of nonlocal games $(G,\psi)$, where $G$ is a two-player one-round game, and $\psi$ is a bipartite state independent of $G$. In the game $(G,\psi)$, the players are allowed to share arbitrarily many…

This article concerns the resolution of impartial combinatorial games, and in particular games that can be split in sums of independent positions. We prove that in order to compute the outcome of a sum of independent positions, it is always…

Given an uncountable subset $\mathcal Y$ of a nonseparable Banach space, is there an uncountable $\mathcal Z\subseteq \mathcal Y$ such that the distances between any two distinct points of $\mathcal Z$ are more or less the same? If an…

We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…

We consider two-player games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequency-related properties: (i) all colors occur with the same asymptotic frequency, (ii) there…

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, for the case where the players are restricted to finite-memory strategies. First, we describe a general framework, where…

We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be…

Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives.…

We study the Maker-Breaker $H$-game played on the edge set of the random graph $G_{n,p}$. In this game two players, Maker and Breaker, alternately claim unclaimed edges of $G_{n,p}$, until all the edges are claimed. Maker wins if he claims…

We define well-connectedness, an order-theoretic notion of largeness whose associated partition relations $\nu\to_{wc}(\mu)_\lambda^2$ formally weaken those of the classical Ramsey relations $\nu\to(\mu)_\lambda^2$. We show that it is…

In this work, we develop a unified framework for establishing sharp threshold results for various Ramsey properties. To achieve this, we view such properties as non-colourability of auxiliary hypergraphs. Our main technical result gives…

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

The language of finite games is used to rephrase Pelant's proof of his result: The separable modification of the complete metric space $C([0,\omega_1])$ is not complete.

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…

Compiling Bell games under cryptographic assumptions replaces the need for physical separation, allowing nonlocality to be probed with a single untrusted device. While Kalai et al. (STOC'23) showed that this compilation preserves quantum…

This paper studies partially observable two-person zero-sum semi-Markov games under a probability criterion, in which the system state may not be completely observed. It focuses on the probability that the accumulated rewards of player 1…