Related papers: When the macroscopic game is the quantum game?

We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then…

A fair gambling is hard to be made between two spatially separated parties without introducing a trusted third party. Here we propose a novel gambling protocol, which enables fair gambling between two distant parties without the help of a…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the…

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

Quantum game theory is the study of strategic behavior by agents with access to quantum technology. Broadly speaking, this technology can be employed in either of two ways: As part of a randomization device or as part of a communications…

We present a two-party protocol for quantum gambling, a new task closely related to coin tossing. The protocol allows two remote parties to play a gambling game, such that in a certain limit it becomes a fair game. No unconditionally secure…

We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular,…

Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms have been developed for…

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.

The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that…

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we…

We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…

We initiate the study of quantum races, games where two or more quantum computers compete to solve a computational problem. While the problem of dueling algorithms has been studied for classical deterministic algorithms, the quantum case…

In a seminal paper, Meyer [David Meyer, Phys. Rev. Lett. 82, 1052 (1999)] described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player…

We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multi-players zero-sum game in which only one player is different from other players, and the game is symmetric for…