Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics

Epperlein, Jeremias; Siegmund, Stefan; Stehlı́k, Petr; Švígler, Vladimír

doi:10.3934/dcdsb.2016.21.803

Cited by 7 publications

(4 citation statements)

References 15 publications

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“…According to the stability theorem and evolutionary stability strategy of replicated dynamic differential equation [24][25], when H(x * 2 ) = 0 and…”

Section: Stability Analysis Of Evolutionary Strategymentioning

confidence: 99%

Evolutionary Game Model of Public Opinion Information Propagation in Online Social Networks

Wang

2020

IEEE Access

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The rapid development of communication technology has greatly changed the way of information propagation. While making use of positive public opinion information in online social networks (OSN) to create value, it is necessary to manage and control the propagation of public opinion. Considering the existence of both positive and negative public opinion, we proposed a tripartite evolutionary game model through identifying the relevant stakeholders involved in the public opinion spreading process, discussed the equilibrium conditions of stakeholders' behavior strategies emphatically and carried out simulation experiments. Then, based on the experimental results, the management strategy and the key intervention points of public opinion spreading were proposed. The result shows that the key to management and control public opinion is realizing the interest balance of all stakeholders. That is, the government should increase the benefits of netizens and media spreading (reporting) positive public opinion, and at the same time strengthen the punishment of them spreading (reporting) negative public opinion. This paper further expands the research of public opinion propagation in OSN, and provides theoretical support and decision-making basis for the management and control of public opinion.

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“…According to the stability theorem and evolutionary stability strategy of replicated dynamic differential equation [24][25], when H(x * 2 ) = 0 and…”

Section: Stability Analysis Of Evolutionary Strategymentioning

confidence: 99%

Evolutionary Game Model of Public Opinion Information Propagation in Online Social Networks

Wang

2020

IEEE Access

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“…Here, we introduce the notation n(i) to represent the set of all of i's neighbors. In the spatial population, player i obtains its objective utility f o i (t) from the interactions with its neighbors n(i) at time step t [59]. For simplicity, the neighbors n(i) of player i are classified into four different groups, namely,…”

Section: Modelmentioning

confidence: 99%

Effects of attitudes on the evolution of cooperation on complex networks

Wang

Chen

2020

J. Stat. Mech.

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This paper considers the utility of each player consisting of two parts: the objective utility and subjective utilities. We assume that a player obtains its objective utility from the interactions with its neighbors in the spatial population. Besides, the subjective utility, which is largely ignored by previous studies, is determined by its attitudes. Here, we focus on how attitudes affect the evolution of cooperation on two different complex networks, the namely square lattice and Barabási–Albert scale-free network. First, the simulations indicate that populations with a higher average attitude can achieve a higher level of cooperation. Furthermore, a positive average attitude is conducive to promoting cooperation, while a negative average attitude leads to a decline in cooperation. Moreover, in populations with a positive average attitude, as the attitude heterogeneity increases, the average level of cooperation decreases. Conversely, in populations with a negative average attitude, increased attitude heterogeneity induces the promotion of cooperation.

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“…Considering a deterministic dynamical system, the natural interest lies in examining the existence and properties of fixed points -strategy vectors X * ∈ S V for which ϕ(t, 0, X * ) = X * for t ∈ N 0 . This topic was studied in [7]. Another notion is the one of a periodic trajectory, a periodic behavior of a game on a graph.…”

Section: Preliminariesmentioning

confidence: 99%

“…Finally, the strategy update is defined by a function ϕ. A general framework of evolutionary games on graphs was developed in [7]. An evolutionary game on a graph can be formally defined as follows.…”

Section: Preliminariesmentioning

confidence: 99%

On arbitrarily long periodic orbits of evolutionary games on graphs

Epperlein¹,

Švígler²

2018

Discrete &Amp; Continuous Dynamical Systems - B

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A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior.1991 Mathematics Subject Classification. Primary: 91A22, 05C57, 91A43; Secondary: 37N40.

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Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics

Cited by 7 publications

References 15 publications

Evolutionary Game Model of Public Opinion Information Propagation in Online Social Networks

Evolutionary Game Model of Public Opinion Information Propagation in Online Social Networks

Effects of attitudes on the evolution of cooperation on complex networks

On arbitrarily long periodic orbits of evolutionary games on graphs

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