### Abstract

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.

Original language | English |
---|---|

Article number | 104914 |

Journal | Communications in Nonlinear Science and Numerical Simulation |

Volume | 79 |

DOIs | |

Publication status | Published - Dec 1 2019 |

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### Keywords

- Control theory
- Evolution of cooperation
- Evolutionary game dynamics
- Public goods game

### ASJC Scopus subject areas

- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics

### Cite this

**Exploring optimal institutional incentives for public cooperation.** / Wang, Shengxian; Chen, Xiaojie; Szolnoki, A.

Research output: Contribution to journal › Article

*Communications in Nonlinear Science and Numerical Simulation*, vol. 79, 104914. https://doi.org/10.1016/j.cnsns.2019.104914

}

TY - JOUR

T1 - Exploring optimal institutional incentives for public cooperation

AU - Wang, Shengxian

AU - Chen, Xiaojie

AU - Szolnoki, A.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Control theory

KW - Evolution of cooperation

KW - Evolutionary game dynamics

KW - Public goods game

UR - http://www.scopus.com/inward/record.url?scp=85069591661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069591661&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2019.104914

DO - 10.1016/j.cnsns.2019.104914

M3 - Article

AN - SCOPUS:85069591661

VL - 79

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 104914

ER -