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The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that…
The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality,…
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…
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…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
A second quantization procedure for the field-theoretic description of interactive games is analyzed. Its relation to the dynamical inverse problem of representation theory is emphasized.
In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a…
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…
The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
This paper introduces a novel framework for modeling interacting humans in a multi-stage game. This "iterated semi network-form game" framework has the following desirable characteristics: (1) Bounded rational players, (2) strategic players…
We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning…
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…
We propose a finite automaton-style solution concept for supergames. In our model, we define an equilibrium to be a cycle of state switches and a supergame to be an infinite walk on states of a finite stage game. We show that if the stage…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…