Managing Catastrophe-bound Industrial Pollution with Game-theoretic Algorithm: the St~Petersburg Initiative

David Yeung ; Leon Petrosyan

Contributions to game theory and management, Tome 1 (2007), pp. 524-538.

Résumé

After several decades of rapid technological advancement and economic growth, alarming levels of pollutions and environmental degradation are emerging all over the world. Reports are portraying the situation as an industrial civilization on the verge of suicide, destroying its environmental conditions of existence with people being held as prisoners on a runaway catastrophe-bound train. Though cooperation in environmental control holds out the best promise of effective action, limited success has been observed. Existing multinational joint initiatives like the Kyoto Protocol can hardly be expected to offer a long-term solution because (i) the plans are limited to a confined set of controls like gas emissions and permits which is unlikely be able to offer an effective mean to reverse the accelerating trend of environmental deterioration, and (ii) there is no guarantee that participants will always be better off and, hence, be committed within the entire duration of the agreement.To create a cooperative solution a comprehensive set of environmental policy instruments including taxes, subsidies, technology choices, pollution abatement activities, pollution legislations and green technology R has to be taken into consideration. The implementation of such a scheme would inevitably bring about different implications in cost and benefit to each of the participating nations. To construct a cooperative solution that every party would commit to from beginning to end, the proposed arrangement must guarantee that every participant will be better-off and the originally agreed upon arrangement remain effective at any time within the cooperative period for any feasible state brought about by prior optimal behavior. This is a “classic” game-theoretic problem. This paper applies the latest discoveries in cooperative game theory and mathematics by researchers at the Center of Game theory in St.Petersburg State University to suggest solutions and means to solve this deadlock problem of global environmental management. Such an approach would yield an effective policy menu to tackle one of the gravest problems facing the global market economy.

Détail

Keywords: Differential games, cooperative solution, subgame consistency, Industrial pollution.

Bibliographie

[1] Basar T., Olsder G. J., Dynamic Noncooperative Game Theory, 2nd Edition, Academic Press, London, 1995 | MR | Zbl

[2] Breton M., Zaccour G., Zahaf M., “A Differential Game of Joint Implementation of Environmental Projects”, Automatica, 41 (2005), 1737–1749 | DOI | MR | Zbl

[3] Breton M., Zaccour G., Zahaf M., “A Game-Theoretic Formulation of Joint Implementation of Environmental Projects”, European Journal of Operational Research, 168 (2006), 221–239 | DOI | MR | Zbl

[4] Dockner E. J., Leitmann G., “Coordinate Transformation and Derivation of Open-Loop Nash Equilibria”, Journal of Economic Dynamics and Control, 110 (2001), 1–15 | MR | Zbl

[5] Dockner E. J., Long N. V., “International Pollution Control: Cooperative Versus Noncooperative Strategies”, Journal of Environmental Economics and Management, 25 (1993), 13–29 | DOI | Zbl

[6] Feenstra T., Kort P. M., De Zeeuw A., “Environmental Policy Instruments in an International Duopoly with Feedback Investment Strategies”, Journal of Economics Dynamics and Control, 25 (2001), 1665–1687 | DOI | MR | Zbl

[7] Fleming W. H., “Optimal Continuous-Parameter Stochastic Control”, SIAM Review, 11 (1969), 470–509 | DOI | MR | Zbl

[8] Fredj K., Martin-Herran G., Zaccour G., “Slowing Deforestation Pace through Subsidies: A Differential Game”, Automatica, 40 (2004), 301–309 | DOI | MR | Zbl

[9] Haurie A., Krawczyk J. B., Roche M., “Monitoring cooperative equilibria in a stochastic differential game”, Journal of Optimization Theory and Applications, 81 (1994), 73–95 | DOI | MR | Zbl

[10] Hurwicz L., “The design of mechanisms for resource allocation”, American Economic Review. Papers and Proceedings, 63 (1973), 1–30 | MR

[11] Jorgensen S., Zaccour G., “Time Consistent Side Payments in a Dynamic Game of Downstream Pollution”, Journal of Economic Dynamics and Control, 25 (2001), 1973–1987 | DOI | MR | Zbl

[12] Maskin E., “Nash Equilibrium and Welfare Optimality”, Review of Economic Studies, 66 (1999), 23–38 | DOI | MR | Zbl

[13] Myerson R., “Mechanisms design”, The New Palgrave: Allocation, Information and Markets, eds. J. Eatwell, M. Milgate, P. Newman, Norton, New York, 1989

[14] Petrosyan L., Yeung D. W. K., “Subgame-consistent Cooperative Solutions in Randomly-furcating Stochastic Differential Games”, International Journal of Mathematical and Computer Modelling, 45, Special Issue on Lyapunov's Methods in Stability and Control (2007), 1294–1307 | DOI | MR | Zbl

[15] Petrosyan L., Zaccour G., “Time-Consistent Shapley Value Allocation of Pollution Cost Reduction”, Journal of Economic Dynamics and Control, 27 (2003), 381–398 | DOI | MR

[16] Singh N., Vives X., “Price and Quantity Competition in a Differentiated Duopoly”, Rand Journal of Economics, 15 (1984), 546–554 | DOI

[17] Stimming M., “Capital Accumulation Subject to Pollution Control: Open-loop versus Feedback Investment Strategies”, Annals of Operations Research, 88 (1999), 309–336 | DOI | MR | Zbl

[18] Tahvonen O., “Carbon Dioxide Abatement as a Differential Game”, European Journal of Political Economy, 10 (1994), 685–705 | DOI

[19] Yeung D. W. K., “A Differential Game of Industrial Pollution Management”, Annals of Operations Research, 37 (1992), 297–311 | DOI | MR | Zbl

[20] Yeung D. W. K., “Dynamically Consistent Cooperative Solution in a Differential Game of Transboundary Industrial Pollution”, Journal of Optimization Theory and Applications, 135:1 (2007) | MR

[21] Yeung D. W. K., Petrosyan L., “Subgame Consistent Cooperative Solutions in Stochastic Differential Games”, Journal of Optimization Theory and Applications, 120 (2004), 651–666 | DOI | MR | Zbl

[22] Yeung D. W. K., Petrosyan L., “Subgame consistent solution of a cooperative stochastic differential game with nontransferable payoffs”, Journal of Optimization Theory and Applications, 2005, 701–724 | DOI | MR | Zbl

[23] Yeung D. W. K., Petrosyan L., “Dynamically Stable Corporate Joint Ventures”, Automatica, 42 (2006), 365–370 | DOI | MR | Zbl

[24] Yeung D. W. K., Petrosyan L., Cooperative Stochastic Differential Games, Springer-Verlag, New York, 2006 | MR

[25] Yeung D. W. K., Petrosyan L., “A Cooperative Stochastic Differential Game of Transboundary Industrial Pollution”, Automatica, 2008

[26] Yeung D. W. K., Petrosyan L., Yeung P. M., “Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs”, Annals of the International Society of Dynamic Games, 9 (2006), 153–170 | DOI | MR