Related papers: When the macroscopic game is the quantum game?
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…
The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and the quantum game of chicken. A phase transition is seen in both games as a function of the entanglement in the game. We observe…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that…
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…
We investigate the quantization of games in which the players can access to a continuous set of classical strategies, making use of continuous-variable quantum systems. For the particular case of the Cournot's Duopoly, we find that, even…
In classical Monty Hall problem, one player can always win with probability 2/3. We generalize the problem to the quantum domain and show that a fair two-party zero-sum game can be carried out if the other player is permitted to adopt…
We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by…
Quantum game theory lays a foundation for understanding the interaction of people using quantum computers with conflicting interests. Recently Zhang proposed a simple yet rich model to study quantum strategic games, and addressed some…
In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium problems…
Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum…
Several quantum versions of the battle of the sexes game are analyzed. Some of them are shown to reproduce the classical game. In some, there are no Nash quantum pure equilibria. In some others, the payoffs are always equal to each other.…
We consider the class of two-person ordinal potential games where each player has the same number of actions $K$. Each game in this class admits at least one pure Nash equilibrium and the best-response dynamics converges to one of these…
We investigate the problem of equilibrium computation for "large" $n$-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we…
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.…
In this work we have introduced two party games with respective winning conditions. One cannot win these games deterministically in the classical world if they are not allowed to communicate at any stage of the game. Interestingly we find…
At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff…
A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to…