The optimal control for promoting the cooperation in evolution game generated by Prisoner's Dilemma

Wang, Xianjia; Dong, Rui; Chen, Lin

doi:10.1016/s0252-9602(17)30118-2

Cited by 10 publications

(5 citation statements)

References 25 publications

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“…In this work, the dynamical system described by the replicator equation is nonlinear, thus it is not easy to obtain the exact expression of the optimal control protocols for institutional incentives in theory [53,54,55]. However, by employing the approach of HJB equation for continuous-time systems, we can succeed in theoretically obtaining the optimal control strategies for institutional incentives.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, optimal control theory [50,51,52] has been introduced to study evolutionary game dynamics [53,54,55], which seems to be an alternative approach for studying the optimal incentive strategy with the minimal cost for the evolution of cooperation. For example Griffin and Belmonte have studied the problem of designing an optimal success tax in a three-species public goods game and formulated the problem as an optimal control problem [53].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore Bravetti and Padilla have introduced an extension of the replicator equation, called the optimal replicator equation, by using optimal control theory [54]. Additionally Wang et al have studied the problem of designing reward and compensation control strategies for promoting the evolution of cooperation in the prisoner's dilemma game [55]. However, it is worth mentioning that these previous works do not involve the investigation of the optimal incentive strategies with the minimal cumulative cost for the evolution of cooperation, and thus it could be interesting to study the optimal strategies of institutional incentives by using optimal control theory.…”

Section: Introductionmentioning

confidence: 99%

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Exploring optimal institutional incentives for public cooperation

Wang

Chen

Szolnoki

2019

Communications in Nonlinear Science and Numerical Simulation

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Prosocial incentive can promote cooperation, but providing incentive is costly. Institutions in human society may prefer to use an incentive strategy which is able to promote cooperation at a reasonable cost. However, thus far few works have explored the optimal institutional incentives which minimize related cost for the benefit of public cooperation. In this work, in combination with optimal control theory we thus formulate two optimal control problems to explore the optimal incentive strategies for institutional reward and punishment respectively. By using the approach of Hamilton-Jacobi-Bellman equation for well-mixed populations, we theoretically obtain the optimal positive and negative incentive strategies with the minimal cumulative cost respectively. Additionally, we provide numerical examples to verify that the obtained optimal incentives allow the dynamical system to reach the desired destination at the lowest cumulative cost in comparison with other given incentive strategies. Furthermore, we find that the optimal punishing strategy is a cheaper way for obtaining an expected cooperation level when it is compared with the optimal rewarding strategy.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring optimal institutional incentives for public cooperation

Wang

Chen

Szolnoki

2019

Communications in Nonlinear Science and Numerical Simulation

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“…This raises an interesting question how we obtain the optimal incentive strategy with the minimal cost. Fortunately, together with evolutionary game theory, optimal control theory provides a systematic framework for studying this problem [43][44][45][46][47][48]. For example, Wang et al studied the optimal control problem for the promotion of cooperation in the prisoner's dilemma [45].…”

mentioning

confidence: 99%

“…Fortunately, together with evolutionary game theory, optimal control theory provides a systematic framework for studying this problem [43][44][45][46][47][48]. For example, Wang et al studied the optimal control problem for the promotion of cooperation in the prisoner's dilemma [45]. Paarporn et al investigated the optimal control policies for evolutionary dynamics with environmental feedback [47].…”

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confidence: 99%

Incentive strategies for the evolution of cooperation: Analysis and optimization

Wang¹,

Liu²,

Chen³

2021

EPL

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How to explain why cooperation can emerge in the real society is one of the most challenging scientific problems. In the past few years, in order to solve the evolutionary puzzle of cooperation, researchers have put forward a variety of solutions and accordingly proposed some mechanisms for the evolution of cooperation. Among them, the implementation of prosocial incentive strategy can increase the benefits of cooperators or reduce the benefits of defectors, which has been regarded as an effective measure to solve the cooperation problem. In this perspective, we provide a mini yet profound review of recent research efforts that explore the roles of incentive strategies in the evolution of cooperation and how to design the optimal incentive protocols to promote the evolution of cooperation more efficiently. Importantly, we show some crucial developments about incentive strategies which have been made in the field and meanwhile come up with some significant routes of further research.

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Research on fractal structure of generalized M–J sets utilized Lyapunov exponents and periodic scanning techniques

Wang¹,

Pei-jun²

2006

Applied Mathematics and Computation

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The optimal control for promoting the cooperation in evolution game generated by Prisoner's Dilemma

Cited by 10 publications

References 25 publications

Exploring optimal institutional incentives for public cooperation

Exploring optimal institutional incentives for public cooperation

Incentive strategies for the evolution of cooperation: Analysis and optimization

Research on fractal structure of generalized M–J sets utilized Lyapunov exponents and periodic scanning techniques

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