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Long studied as a toy model, quantum zero-sum games have recently resurfaced as a canonical playground for modern areas such as non-local games, quantum interactive proofs, and quantum machine learning. In this simple yet fundamental…
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…
In quantum information, nonlocal games are particularly useful for differentiating classical, quantum, and non-signalling correlations. An example of differentiation is given by the principle of no-collapse of communication complexity,…
Graph games with {\omega}-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and 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…
We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given…
Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no -…
Research in quantum games has flourished during recent years. However, it seems that opinion remains divided about their true quantum character and content. For example, one argument says that quantum games are nothing but 'disguised'…
Energy games belong to a class of turn-based two-player infinite-duration games}played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in ${\sf NP} \cap {\sf co\mbox{-}NP}$, but are not…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
Nonlocal quantum games provide proof of principle that quantum resources can confer advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent…
We show a relation, based on parallel repetition of the Magic Square game, that can be solved, with probability exponentially close to $1$ (worst-case input), by $1D$ (uniform) depth $2$, geometrically-local, noisy (noise below a…
We investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan,…
Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in…
We study generalized Nash equilibrium (GNE) problems in games with quadratic costs and individual linear equality constraints. Departing from approaches that require strong monotonicity and/or shared constraints, we reformulate the KKT…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
Games on graphs provide the appropriate framework to study several central problems in computer science, such as the verification and synthesis of reactive systems. One of the most basic objectives for games on graphs is the liveness (or…
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 address the question of when quantum entanglement is a useful resource for information processing tasks by presenting a new class of nonlocal games that are simple, direct, generalizations of the Clauser Horne Shimony Holt game. For some…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…