##
**Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution.**
*(English)*
Zbl 1210.91098

Summary: This paper presents a cooperative differential game of transboundary industrial pollution. A noted feature of the game model is that the industrial sectors remain competitive among themselves while the governments cooperate in pollution abatement. It is the first time that time consistent solutions are derived in a cooperative differential game on pollution control with industries and governments being separate entities. A stochastic version of the model is presented and a subgame-consistent cooperative solution is provided. This is the first study of pollution management in a stochastic differential game framework.

### MSC:

91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |

91A23 | Differential games (aspects of game theory) |

91A12 | Cooperative games |

PDF
BibTeX
XML
Cite

\textit{D. W. K. Yeung}, J. Optim. Theory Appl. 134, No. 1, 143--160 (2007; Zbl 1210.91098)

Full Text:
DOI

### References:

[1] | Yeung, D.W.K.: A differential game of industrial pollution management. Ann. Oper. Res. 37, 297–311 (1992) · Zbl 0789.90103 |

[2] | Dockner, E.J., Long, N.V.: International pollution control: cooperative versus noncooperative strategies. J. Environ. Econ. Manag. 25, 13–29 (1993) · Zbl 0775.90309 |

[3] | Tahvonen, O.: Carbon dioxide abatement as a differential game. Eur. J. Political Econ. 10, 685–705 (1994) |

[4] | Stimming, M.: Capital accumulation subject to pollution control: open-loop versus feedback investment strategies. Ann. Oper. Res. 88, 309–336 (1999) · Zbl 0932.91040 |

[5] | Feenstra, T., Kort, P.M., De Zeeuw, A.: Environmental policy instruments in an international duopoly with feedback investment strategies. J. Econ. Dyn. Control 25, 1665–1687 (2001) · Zbl 1056.91541 |

[6] | Jørgensen, S., Zaccour, G.: Time consistent side payments in a dynamic game of downstream pollution. J. Econ. Dyn. Control 25, 1973–1987 (2001) · Zbl 0978.91018 |

[7] | Fredj, K., Martín-Herrán, G., Zaccour, G.: Slowing deforestation pace through subsidies: a differential game. Automatica 40, 301–309 (2004) · Zbl 1043.92037 |

[8] | Breton, M., Zaccour, G., Zahaf, M.: A differential game of joint implementation of environmental projects. Automatica 41, 1737–1749 (2005) · Zbl 1125.91309 |

[9] | Breton, M., Zaccour, G., Zahaf, M.: A game-theoretic formulation of joint implementation of environmental projects. Eur. J. Oper. Res. 168, 221–239 (2006) · Zbl 1131.91370 |

[10] | Petrosyan, L., Zaccour, G.: Time-consistent Shapley value allocation of pollution cost reduction. J. Econ. Dyn. Control 27, 381–398 (2003) · Zbl 1027.91005 |

[11] | Yeung, D.W.K., Petrosyan, L.: Subgame consistent cooperative solutions in stochastic differential games. J. Optim. Theory Appl. 120, 651–666 (2004) · Zbl 1140.91321 |

[12] | Dixit, A.K.: A model of duopoly suggesting a theory of entry barriers. Bell J. Econ. 10, 20–32 (1979) |

[13] | Singh, N., Vives, X.: Price and quantity competition in a differentiated duopoly. Rand J. Econ. 15, 546–554 (1984) |

[14] | Isaacs, R.: Differential Games. Wiley, New York (1965) · Zbl 0125.38001 |

[15] | Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957) · Zbl 0077.13605 |

[16] | Nash, J.F.: Non-cooperative games. Ann. Math. 54, 286–295 (1951) · Zbl 0045.08202 |

[17] | Yeung, D.W.K.: A cooperative differential game of transboundary industrial pollution management. Institute for Enterprise Development and Management Research Working Papers, No. WP-200702, HKBU (2007). Available at www.hkbu.edu.hk/\(\sim\)iedmr |

[18] | Yeung, D.W.K., Petrosyan, L.: Dynamically stable corporate joint ventures. Automatica 42, 365–370 (2006) · Zbl 1136.91320 |

[19] | Yeung, D.W.K., Petrosyan, L.: Cooperative stochastic differential games. Springer, New York (2006b) · Zbl 1108.91002 |

[20] | Fleming, W.H.: Optimal continuous-parameter stochastic control. SIAM Rev. 11, 470–509 (1969) · Zbl 0192.52501 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.