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A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
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.…
This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is also discussed. The review is addressed to…
Most algorithmic studies on multi-agent information design so far have focused on the restricted situation with no inter-agent externalities; a few exceptions investigated truly strategic games such as zero-sum games and second-price…
We extend the concept of a classical two-person static game to the quantum domain, by giving an Hilbert structure to the space of classical strategies and studying the Battle of the Sexes game. We show that the introduction of entangled…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Whether uniquely quantum resources confer advantages in fully classical, competitive environments remains an open question. Competitive zero-sum reinforcement learning is particularly challenging, as success requires modelling dynamic…
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…
The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally…
This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to…
Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs)…
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…
A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…
The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative game. In both cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved.
On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is…
A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal profits in such the games is considered.…
In game theory, a popular model of a struggle for survival among three competing agents is a truel, or three person generalization of a duel. Adopting the ideas recently developed in quantum game theory, we present a quantum scheme for the…