Related papers: von Neumann's Minimax Theorem for Continuous Quant…
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…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
In the second part of our work on observables we have shown that quantum observables in the sense of von Neumann, i.e.bounded selfadjoint operators in some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded continuous…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by…
Weaver has recently defined the notion of a quantum relation on a von Neumann algebra. We demonstrate that the corresponding notion of a quantum function between two von Neumann algebras coincides with that of a normal unital…
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…
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…
Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of quantum mechanics (QM). Within this theory dispersion free ensembles do not exist. To accommodate a theory of quantum mechanics that allow dispersion free…
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…
Soon after the dawn of quantum error correction, DiVincenzo and Peres observed that stabilizer codewords could give rise to simple proofs of quantumness via contextuality. This discovery can be recast in the language of nonlocal games:…
Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…
Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely…
While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting--in…
We study a pursuit-evasion differential game with finite number of pursuers and one evader in Hilbert space with geometric constraints on the control functions of players. We solve the game by presenting explicit strategies for pursuers…