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New Journal of Physics

Evolution of quantum and classical strategies on networks by group interactions

Qiang Li, Azhar Iqbal, Minyou Chen, Derek Abbott

Published Oct 19, 2012• 17 citations
Publisher

Abstract

In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum and classical strategies on networks in the public goods game. Comparing the results of evolution on a scale-free network and a square lattice, we find that a quantum strategy outperforms the classical strategies, regardless of the network. Moreover, a quantum strategy dominates the population earlier in group interactions than it does in pairwise interactions. In particular, if the hub node in a scale-free network is occupied by a cooperator initially, the strategy of cooperation will prevail in the population. However, in other situations, a quantum strategy can defeat the classical ones and finally becomes the dominant strategy in the population.

DOI
10.1088/1367-2630/14/10/103034

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In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum and classical strategies on networks in the public goods game. Comparing the results of evolution on a scale-free network and a square lattice, we find that a quantum strategy outperforms the classical strategies, regardless of the network. Moreover, a quantum strategy dominates the population earlier in group interactions than it does in pairwise interactions. In particular, if the hub node in a scale-free network is occupied by a cooperator initially, the strategy of cooperation will prevail in the population. However, in other situations, a quantum strategy can defeat the classical ones and finally becomes the dominant strategy in the population.
In this paper, we focus on how to solve complex traditional game problems with quantum technology. Quantum game prompts the emergence of cooperation by introducing the quantum strategy to traditional game. We analyze three important factors of the evolutionary quantum game on lattice networks: steps, temptation and entanglement. Results of the experimental applications of analysis procedure are given to illustrate the proposed quantum technique. The system of quantum game will show signs of stability after a series of transient steps. We will reap better benefit by choosing appropriate quantum parameters, because quantum strategys advantage over defeat strategy.
We study the impact of adaptive degrees of trust on the evolution of cooperation in the quantum prisoner's dilemma game. In addition to the strategies, links between players are also subject to evolution. Starting with a scale-free interaction network, players adjust trust towards their neighbors based on received payoffs. The latter governs the strategy adoption process, while trust governs the rewiring of links. As soon as the degree of trust towards a neighbor drops to zero, the link is rewired to another randomly chosen player within the network. We find that for small temptations to defect cooperators always dominate, while for intermediate and strong temptations a single quantum strategy is able to outperform all other strategies. In general, reciprocal trust remains within close relationships and favors the dominance of a single strategy. Due to coevolution, the power-law degree distributions transform to Poisson distributions.
By incorporating payoff matrix and population evolution of open systems and proposing density games, pioneering effort has been made to break the following two basic assumptions of evolutionary game theory over the past decades: the payoff from the game determines the reproductive rate of individuals, and the total population size remains constant by a variable called the death rate. On the other hand, most studies on strategic interactions in game theories consider independent individual strategies as the basic unit of analyses. This is in fact not always true in human interaction strategies. It has been unclear that how subjective non-independent species with strategic interactions in open dynamic systems evolve. In this paper, we create the new concept of hybrid quantum games, and propose an open quantum dynamic symbiosis model for exploring the evolution of this type of species under unclosed social settings. We show that the stability conditions of the model with non-independent strategic interactions are influenced by the specific symbiosis states, game payoff matrix and quantum entanglement. The stability conditions of the competition scenario are more stringent than those of the cooperation one. Our system dynamics simulation study demonstrates and verifies the dynamic changes for the population sizes of two different species in the theoretical model, on the basis of the stability conditions of the competition and cooperation scenarios. Our model combines quantum games, game payoff matrix and symbiosis equations organically, and can provide insights into competition, cooperation and symbiosis mechanisms in open systems with subjective non-independent strategies considered.
The authors proposed a quantum Prisoner's Dilemma (PD) game as a natural extension of the classic PD game to resolve the dilemma. Here, we establish a new Nash equilibrium principle of the game, propose the notion of convergence and discover the convergence and phase-transition phenomena of the evolutionary games on networks. We investigate the many-body extension of the game or evolutionary games in networks. For homogeneous networks, we show that entanglement guarantees a quick convergence of super cooperation, that there is a phase transition from the convergence of defection to the convergence of super cooperation, and that the threshold for the phase transitions is principally determined by the Nash equilibrium principle of the game, with an accompanying perturbation by the variations of structures of networks. For heterogeneous networks, we show that the equilibrium frequencies of super-cooperators are divergent, that entanglement guarantees emergence of super-cooperation and that there is a phase transition of the emergence with the threshold determined by the Nash equilibrium principle, accompanied by a perturbation by the variations of structures of networks. Our results explore systematically, for the first time, the dynamics, morphogenesis and convergence of evolutionary games in interacting and competing systems.
We present a study of a dynamical quantum game. Each agent has a `memory' of her performance over the previous m timesteps, and her strategy can evolve in time. The game exhibits distinct regimes of optimality. For small m the classical game performs better, while for intermediate m the relative performance depends on whether the source of qubits is `corrupt'. For large m , the quantum players dramatically outperform the classical players by `freezing' the game into high-performing attractors in which evolution ceases.