Related papers: Quantum Game with Restricted Matrix Strategies

In this letter we show that communication when restricted to a single information carrier (i.e. single particle) and finite speed of propagation is fundamentally limited for classical systems. On the other hand, quantum systems can surpass…

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

We consider a game in which each player must find a compromise between more daring strategies that carry a high risk for him to be eliminated, and more cautious ones that, however, reduce his final score. For two symmetric players this game…

We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random…

We outline the general construction of three-players games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the exchange of the players; (ii) the existence of the upper bound for total payoff…

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…

The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable that the other one. Using the Cournot's duopoly example we…

We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which…

We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…

In this paper, I prove that existence of pure-strategy Nash equilibrium in games with infinitely many players is equivalent to the axiom of choice.

In a one-off Minority game, when a group of players agree to collaborate they gain an advantage over the remaining players. We consider the advantage obtained in a quantum Minority game by a coalition sharing an initially entangled state…

We investigate quantum games in which the information is asymmetrically distributed among the players, and find the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement, but…

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.…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

The number of Nash equilibria of the mixed extension of a generic finite game in normal form is finite and odd. This raises the question how large the number can be, depending on the number of players and the numbers of their pure…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…

The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality,…

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by…

Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games.…