Related papers: Kuhn's Equivalence Theorem for Games in Intrinsic …
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
Video game playing is an extremely structured domain where algorithmic decision-making can be tested without adverse real-world consequences. While prevailing methods rely on image inputs to avoid the problem of hand-crafting state space…
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…
We consider repeated games where the players behave according to cumulative prospect theory (CPT). We show that, when the players have calibrated strategies and behave according to CPT, the natural analog of the notion of correlated…
The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game --…
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…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
The so called \emph{quantum game theory} has recently been proclaimed as one of the new branches in the development of both quantum information theory and game theory. However, the notion of a quantum game itself has never been strictly…
Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, etc.), bisimilarity has been extended in various ways:…
We prove that an imitation game has a perfect quantum approximate strategy if and only if there exists a bi-tracial state on the minimal tensor product of two universal C${^*}$-algebras, which induces the perfect correlation. Moreover, we…
Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
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…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
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…
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…