Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

Guo, Ping; Wang, Yuzhen; Li, Haitao

doi:10.1016/j.automatica.2013.08.008

Cited by 137 publications

(54 citation statements)

References 26 publications

(27 reference statements)

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“…Combining the above deduction with (11) and (12) in Lemma 3, we conclude that (14) holds for t = t 0 + 1 and then by induction holds for any t ≥ t 0 . In fact, a much stronger statement than Proposition 1 can be made, which shows the invariant state/set is also globally attractive.…”

Section: Proof: For a Biased Population It Holds Thatmentioning

confidence: 80%

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Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

Ramazi

Cao

2018

IEEE Trans. Automat. Contr.

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Abstract-To study how sustainable cooperation might emerge among self-interested interacting individuals, we investigate the long-run behavior of the decision-making dynamics in a finite, well-mixed population of individuals, who play collectively over time a population game. Repeatedly each individual is activated asynchronously to update her decision to either cooperate or defect according to the myopic best-response rule. The game's payoff matrices, chosen to be those of either prisoner's dilemma or snowdrift games to underscore cooperation-centered social dilemmas, are fixed, but can be distinct for different individuals. So the overall population is heterogeneous. We first classify such heterogeneous individuals into different types according to their cooperating tendencies stipulated by their payoff matrices. Then we show that no matter what initial strategies the individuals decide to use, surprisingly one can always identify one type of individuals as a benchmark such that after a sufficiently long but finite time, individuals more cooperative compared to the benchmark always cooperate while those less cooperative compared to the benchmark defect. When such fixation takes place, the total number of cooperators in the population either becomes fixed or fluctuates at most by one. Such insight provides theoretical explanation for some complex behavior recently reported in simulation studies that highlight the puzzling effect of individuals' heterogeneity on collective decision-making dynamics.

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Section: Proof: For a Biased Population It Holds Thatmentioning

confidence: 80%

“…So from Lemma 1 we know that if an SD i , i > k p , agent is active at t 0 , her strategy at t 0 + 1 remains to defect, which proves (11). Now we prove (12). At x n SDj ) = n * SD kp (5) = ⇒ n C (t 0 ) < n * SD kp −1…”

Section: B Proof Of Lemmamentioning

confidence: 99%

Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

Ramazi

Cao

2018

IEEE Trans. Automat. Contr.

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“…A normal evolutionary networked game consists of three basic components [25,29]: (ii) A two-person symmetric game at each period G := (S, A), where S := {s 1 , s 2 , . .…”

Section: Evolutionary Networked Game Modelmentioning

confidence: 99%

“…Up to now, many fundamental results have been presented for the analysis and control of Boolean networks [13][14][15][16][17][18][19][20][21], the coloring problem [22], the design of shifting register [23], the fault detection [24], and so on. In addition, since the dynamics of a finite game can be modeled as a logical network [25], the semi-tensor product method has also been applied to the study of game theory [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Stable degree analysis for strategy profiles of evolutionary networked games

Guo

Wang

2016

Sci. China Inf. Sci.

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In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with "best imitate" strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.

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“…In addition, the STP method has reached some meaningful conclusions on probabilistic logical networks, such as [24][25][26][27][28][29][30][31][32][33] . Furthermore, it is noted that the STP tool has been used in the investigation of game theory [34,35] . In [34] , the STP was used to formulate NEGs and a kind of algebraic expression was obtained.…”

Section: Introductionmentioning

confidence: 99%

A matrix approach to modeling and optimization for dynamic games with random entrance

Zhao

Wang

2016

Applied Mathematics and Computation

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Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

Cited by 137 publications

References 26 publications

Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

Stable degree analysis for strategy profiles of evolutionary networked games

A matrix approach to modeling and optimization for dynamic games with random entrance

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