Related papers: An explicit classical strategy for winning a $\mat…

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…

In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of…

This paper introduces a class of games, called unit-sphere games, where strategies are real vectors with unit 2-norms (or, on a unit-sphere). As a result, they can no longer be interpreted as probability distributions over actions, but…

Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept…

We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…

Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between…

Local simultaneous state discrimination (LSSD) is a recently introduced problem in quantum information processing. Its classical version is a non-local game played by non-communicating players against a referee. Based on a known probability…

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…

A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…

We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants…

The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…

Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the…

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over…

It is known that the generalized Nash equilibrium problem can be reformulated as a quasivariational inequality. Our aim in this work is to introduce a variational approach to study the existence of solutions for generalized ordinal Nash…

We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…

The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum…

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given…

Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…

The two-players $N$ strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem of finding a general form of gate…