Related papers: Perfect Quantum Approximate Strategies for Imitati…

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…

We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to…

Imitation sometimes achieves success in multi-agent situations even though it is very simple. In game theory, success of imitation has been characterized by unbeatability against other agents. Previous studies specified conditions under…

Robust self-testing in non-local games allows a classical referee to certify that two untrustworthy players are able to perform a specific quantum strategy up to high precision. Proving robust self-testing results becomes significantly…

We develop an abstract operator-algebraic characterization of robust self-testing for synchronous correlations and games. Specifically, we show that a synchronous correlation is a robust self-test if and only if there is a unique state on…

We characterize exact, and approximate, optimality of games that players can interact with using quantum strategies. In comparison to a previous work of the author, arXiv: 2311.12887, which applied a 2016 framework due to Ostrev for…

A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…

Games are natural models for multi-agent machine learning settings, such as generative adversarial networks (GANs). The desirable outcomes from algorithmic interactions in these games are encoded as game theoretic equilibrium concepts, e.g.…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…

A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…

We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…

Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilised as a mechanism to witness and determine…

Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called "Bell inequality violations." We give two new two-player games with Bell inequality violations that…

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…

We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor…

Quantum guessing games form a versatile framework for studying different tasks of information processing. A quantum guessing game with posterior information uses quantum systems to encode messages and classical communication to give partial…

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…

A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…