Related papers: Efficiency and formalism of quantum games
The physical world obeys the rules of quantum, as opposed to classical, physics. Since the playing of any particular game requires physical resources, the question arises as to how Game Theory itself would change if it were extended into…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we…
Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players,…
The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
The concept of a classical player, corresponding to a classical random variable, is extended to include quantum random variables in the form of self adjoint operators on infinite dimensional Hilbert space. A quantum version of Von Neumann's…
We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that…
We introduce a general representation of large-population games in which each player s influence ON the others IS centralized AND limited, but may otherwise be arbitrary.This representation significantly generalizes the class known AS…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…
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…
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…
Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…
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 show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding…
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…