Coevolution of Quantum and Classical Strategies on Evolving Random Networks

Li, Qiang; Iqbal, Azhar; Perc, Matjaž; Chen, Minyou; Abbott, Derek

doi:10.1371/journal.pone.0068423

Cited by 36 publications

(10 citation statements)

References 88 publications

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“…Second, researchers have questioned whether the two-dimensional grid is an adequate description of real world interpersonal and biological networks, and have extended the model to investigate more complex network structures [ 15 ] such as regular random graphs [ 15 – 18 ], small-world networks [ 16 , 19 , 20 ], or scale-free networks [ 18 , 21 – 23 ]. Indeed, related studies have considered dynamic models of interaction for networks of binary ties (e.g., [ 24 – 27 ]), ties that varied in strength over time (e.g., [ 28 – 30 ]), and ties that also change positive or negative valence over time [ 31 ]. Third, recent work has questioned whether Nowak and May’s rule for local replication—that is, imitation of the fittest neighbor—is an accurate description of the diffusion of strategies.…”

Section: Introductionmentioning

confidence: 99%

Greed and Fear in Network Reciprocity: Implications for Cooperation among Organizations

et al. 2016

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Extensive interdisciplinary literatures have built on the seminal spatial dilemmas model, which depicts the evolution of cooperation on regular lattices, with strategies propagating locally by relative fitness. In this model agents may cooperate with neighbors, paying an individual cost to enhance their collective welfare, or they may exploit cooperative neighbors and diminish collective welfare. Recent research has extended the model in numerous ways, incorporating behavioral noise, implementing other network topologies or adaptive networks, and employing alternative dynamics of replication. Although the underlying dilemma arises from two distinct dimensions—the gains for exploiting cooperative partners (Greed) and the cost of cooperating with exploitative partners (Fear)–most work following from the spatial dilemmas model has argued or assumed that the dilemma can be represented with a single parameter: This research has typically examined Greed or Fear in isolation, or a composite such as the K-index of Cooperation or the ratio of the benefit to cost of cooperation. We challenge this claim on theoretical grounds—showing that embedding interaction in networks generally leads Greed and Fear to have divergent, interactive, and highly nonlinear effects on cooperation at the macro level, even when individuals respond identically to Greed and Fear. Using computational experiments, we characterize both dynamic local behavior and long run outcomes across regions of this space. We also simulate interventions to investigate changes of Greed and Fear over time, showing how model behavior changes asymmetrically as boundaries in payoff space are crossed, leading some interventions to have irreversible effects on cooperation. We then replicate our experiments on inter-organizational network data derived from links through shared directors among 2,400 large US corporations, thus demonstrating our findings for Greed and Fear on a naturally-occurring network. In closing, we discuss implications of our main findings regarding Greed and Fear for the problem of cooperation on inter-organizational networks.

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Section: Introductionmentioning

confidence: 99%

Greed and Fear in Network Reciprocity: Implications for Cooperation among Organizations

et al. 2016

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“…As classical probabilities, quantum probabilities are normalized but they also obey other constraints that are dictated by the rules of quantum mechanics. Our earlier studies [58,59] have investigated coevolution [65] in quantum games and also developing a probabilistic approach to quantum games [24,48,50,60]. The solution concept of the Nash equilibrium (NE) from non-cooperative game theory [66][67][68] has been studied from the outset of the field of quantum game theory.…”

Section: Introductionmentioning

confidence: 99%

Social optimality in quantum Bayesian games

Iqbal

Chappell

Abbott

2015

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• Study game-theoretic solution concept of social optimality in a quantum Bayesian game. • Our quantum Bayesian game uses the setting of generalized EPR experiments. • A new stronger socially optimal outcome emerges in the quantum Bayesian game. a b s t r a c tA significant aspect of the study of quantum strategies is the exploration of the gametheoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria. A refinement on the set of Pareto optimal outcomes is known as social optimality in which the sum of players' payoffs is maximized. This paper analyzes social optimality in a Bayesian game that uses the setting of generalized Einstein-Podolsky-Rosen experiments for its physical implementation. We show that for the quantum Bayesian game a direct connection appears between the violation of Bell's inequality and the social optimal outcome of the game and that it attains a superior socially optimal outcome.

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“…The collective social behavior of large communities of individuals, such as culture dissemination, rumor spreading and the dynamics of opinion formation are widely studied using the concepts and methods of statistical physics [7][8][9][10]. Network science provides a very effective method to explore the collective social behavior [11][12][13][14][15].…”

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confidence: 99%

Opinion dynamics in activity-driven networks

Li¹,

Han²,

Ma³

et al. 2017

EPL

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PACS 89.75.-k-Complex systems PACS 89.75.Fb-Structures and organization in complex systems PACS 89.75.Hc-Networks and genealogical trees Abstract-Social interaction between individuals constantly affects the development of their personal opinions. Previous models such as the Deffuant model and the Hegselmann-Krause (HK) model have assumed that individuals only update their opinions after interacting with neighbors whose opinions are similar to their own. However, people are capable of communicating widely with all of their neighbors to gather their ideas and opinions, even if they encounter a number of opposing attitudes. We propose a model in which agents listen to the opinions of all their neighbors. Continuous opinion dynamics are investigated in activity-driven networks with a tolerance threshold. We study how the initial opinion distribution, tolerance threshold, opinionupdating speed, and activity rate affect the evolution of opinion. We find that when the initial fraction of positive opinion is small, all opinions become negative by the end of the simulation. As the initial fraction of positive opinions rises above a certain value-about 0.45-the final fraction of positive opinions sharply increases and eventually equals 1. Increased tolerance threshold δ is found to lead to a more varied final opinion distribution. We also find that if the negative opinion has an initial advantage, the final fraction of negative opinion increases and reaches its peak as the updating speed λ approaches 0.5. Finally we show that the lower the activity rate of individuals, the greater the fluctuation range of their opinions.

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Coevolution of Quantum and Classical Strategies on Evolving Random Networks

Cited by 36 publications

References 88 publications

Greed and Fear in Network Reciprocity: Implications for Cooperation among Organizations

Greed and Fear in Network Reciprocity: Implications for Cooperation among Organizations

Social optimality in quantum Bayesian games

Opinion dynamics in activity-driven networks

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