To explore the influence of quantum information on the common social problem of honesty and trickery, we propose a Bayesian model for the quantum prisoners’ dilemma game. In this model, the players’ strategy formation is regarded as a negotiation of their move contract based on their types of decision policies, honesty or trickery. Although the implementation of quantum information cannot eliminate tricky players, players in our model can always end up with higher payoffs than in the classical game. For a good proportion of a credibility parameter value, a rational player will take an honest action, which is in remarkable contrast to the observation that players tend to defect in the classical prisoners’ dilemma game. This research suggests that honesty will be promoted to enhance cooperation with the assistance of quantum information resources.
To explore the influence of quantum information on the common social problem of honesty and trickery, we propose a Bayesian model for the quantum prisoners’ dilemma game. In this model, the players’ strategy formation is regarded as a negotiation of their move contract based on their types of decision policies, honesty or trickery. Although the implementation of quantum information cannot eliminate tricky players, players in our model can always end up with higher payoffs than in the classical game. For a good proportion of a credibility parameter value, a rational player will take an honest action, which is in remarkable contrast to the observation that players tend to defect in the classical prisoners’ dilemma game. This research suggests that honesty will be promoted to enhance cooperation with the assistance of quantum information resources.
Decision-making by the two negotiating parties is simulated by a prisoner's dilemma game.The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options.Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state.The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized.On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair.We show that quantum prisoner's dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions.Some economical examples of utilizing quantum game Nash equilibria are proposed.
This paper applies quantum game theory to three ethical dilemmas that frequently arise in negotiation: cooperation versus competition, self-interest versus equity, and honesty versus deception. Using quantum extensions of selected games such as the Prisoner's Dilemma, the Ultimatum Game, the Battle of the Sexes, and the Buyer-Seller Game, we examine whether quantization can generate equilibria that improve classical outcomes while also aligning more closely with ethical principles such as fairness, cooperation, and honesty. The analysis shows that quantum strategies, through entanglement and superposition, can sustain cooperative, fair, or honest behaviour as stable equilibria, outcomes that are typically unstable or unattainable in classical settings. The specific outcomes depend on the chosen quantization method, but across cases, the analysis consistently shows that quantum formulations expand the range of solutions in which efficiency and ethical principles co-exist.
In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.
What happens when an infinite number of players play a quantum game? In this paper, 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 will use the numerical agent-based model (ABM) and compare it with the analytical Nash equilibrium mapping (NEM) technique. To measure cooperation, we consider five indicators, i.e., game magnetization, entanglement susceptibility, correlation, player’s payoff average, and payoff capacity, respectively. In quantum social dilemmas, entanglement plays a non-trivial role in determining the behavior of the quantum players (or qubits) in the thermodynamic limit, and for QuPD, we consider the existence of bipartite entanglement between neighboring quantum players. For the five indicators in question, we observe first-order phase transitions at two entanglement values, and these phase transition points depend on the payoffs associated with the QuPD game. We numerically analyze and study the properties of both the quantum and the defect phases of the QuPD via the five indicators. The results of this paper demonstrate that both ABM and NEM, in conjunction with the chosen five indicators, provide insightful information on cooperative behavior in an infinite-player one-shot quantum prisoner’s dilemma.
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 the actions or beliefs of the other player. Each takes actions which maximize their expected utility and revises their beliefs with the classical Bayes rule between rounds. We simulate iterated play to see if and how players can learn about the presence of shared entanglement and to explore how their performance, their beliefs, and the game's structure interrelate. In the CHSH game, we find that players can learn that entanglement is present and use this to achieve quantum advantage. We find that they can only do so if they also believe the other player will act correctly to exploit the entanglement. In the case of low or zero entanglement in the CHSH game, the players cannot achieve quantum advantage, even in the case where they believe the entanglement is higher than it is. For the prisoners dilemma, we show that assuming 1-fold rational players (rational players who believe the other player is also rational) reduces the quantum extension [Eisert, Wilkens, and Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)] of the prisoners dilemma to a game with only two strategies, one of which (defect) is dominant for low entanglement, and the other (the quantum strategy Q) is dominant for high entanglement. For intermediate entanglement, neither strategy is dominant. We again show that players can learn entanglement in iterated play. We also show that strong belief in entanglement causes optimal play even in the absence of entanglement -- showing that belief in entanglement is acting as a proxy for the players trusting each other. Our work points to possible future applications in resource detection and quantum algorithm design.
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 combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game. By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared among the parties. It is seen that the strategies of the players act as carriers of information in quantum games.