Related papers: Risk-Dominant Equilibrium in Quantum Prisoner's Di…
In a recent paper, Eisert et al. presented a quantum mechanical generalization of Prisoner's Dilemma. They asserted that the maximally entangled game exhibits a unique Nash equilibrium which yields a pay-off equivalent to cooperative…
This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. The quantization process involves extending the classical game by introducing two additional unitary strategies. We consider five…
We investigate the 3-player quantum Prisoner's Dilemma with a certain strategic space, a particular Nash equilibrium that can remove the original dilemma is found. Based on this equilibrium, we show that the game is enhanced by the…
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…
Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner's dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD…
In the quantum version of prisoners' dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducing a third qubit that the interrogator can entangle with the…
The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple…
The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and the quantum game of chicken. A phase transition is seen in both games as a function of the entanglement in the game. We observe…
The well known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results…
We investigate quantum strategy in moving frames by considering Prisoner's Dilemma and propose four thresholds of $\gamma$ for two players to determine their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in…
What happens when an infinite number of players play a quantum game? In this tutorial, we will answer this question by looking at the emergence of cooperation, in the presence of noise, in a one-shot quantum Prisoner's dilemma (QuPD). We…
We apply a Bayesian agent-based framework inspired by QBism to iterations of two quantum games, the CHSH game and the quantum prisoners' dilemma. In each two-player game, players hold beliefs about an amount of shared entanglement and about…
We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which…
We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $\gamma $. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it…
We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different…
The properties of the Cournot model based on the most general entanglement operator containing quadratic expressions which is symmetric with respect to the exchange of players are considered. The degree of entanglement of games dependent on…
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
Under the assumption of complete rationality, Nash equilibrium is the only reasonable strategy (set) of the finitely repeated prisoner's dilemma. In fact, some strategies only slightly deviate from the so-called rationality, and the…
Effects of classical/quantum correlations and operations in game theory are analyzed using Samaritan's Dilemma. We observe that introducing either quantum or classical correlations to the game results in the emergence of a unique or…
In its normal form prisoners' dilemma (PD) is represented by a payoff matrix showing players strategies and payoffs. To obtain distinguishing trait and strategic form of PD certain constraints are imposed on the elements of its payoff…