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In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent…

The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring…

The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple…

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…

Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…

We develop a constrained bimatrix game framework that can be used to model many practical problems in many disciplines, including jamming in packetized wireless networks. In contrast to the widely used zero-sum framework, in bimatrix games…

A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality…

In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his…

A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the…

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium…

Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game…

Motivated by the recent success of reinforcement learning in games such as Go and Dota2, we formulate Bell non-local games as a reinforcement learning problem. Such a formulation helps us to explore Bell non-locality in a range of…

We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…

We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state…

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it…

We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of Quantum Operations on a particular system, we use Kraus operators as quantum strategies. The physical…