相关论文: Nonlocal Games, Compression Theorems, and the Arit…

We review the correspondence between synchronous games and their associated $*$-algebra. Building upon the work of (Helton et al., New York J. Math. 2017), we propose results on algebraic and locally commuting graph identities. Based on the…

We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…

Gradient-based algorithms have shown great promise in solving large (two-player) zero-sum games. However, their success has been mostly confined to the low-precision regime since the number of iterations grows polynomially in $1/\epsilon$,…

Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of $n$ players with 0-1 valued…

Non-local games are an important part of quantum information processing. Recently there has been an increased interest in generalizing non-local games beyond the basic setup by considering games with multiple parties and/or with large…

We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…

This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchical sub-games at each iteration level. Building upon Alpay…

Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…

We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in $\textbf{NP} \cap \textbf{coNP}$…

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…

We study no-signalling correlations over Cantor spaces, placing the product of infinitely many copies of a finite non-local game in a unified general setup. We define the subclasses of local, quantum spatial, approximately quantum and…

Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…

We consider the natural extension of two-player nonlocal games to an arbitrary number of players. An important question for such nonlocal games is their behavior under parallel repetition. For two-player nonlocal games, it is known that…

The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every…

The Hanoi Omega-Automata (HOA) format has established itself as the definitive standard for encoding $\omega$-regular automata in modern synthesis tools. While HOA is widely adopted due to its succinct symbolic representation, using Boolean…

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a…

We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization of whether or not a mirror game has perfect commuting…

Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…

We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect…