Differential Game of Pollution Control with Overlapping Generations
Contributions to game theory and management, Tome 5 (2012), pp. 310-320.

Voir la notice de l'article provenant de la source Math-Net.Ru

We formulate an overlapping generations model on optimal emissions with continuous age-structure. We compare the non-cooperative solution to the cooperative one and obtain fundamental differences in the optimal strategies. Also including an altruistic motive does not avoid the problem of the myopic non-cooperative solution. Finally we define a time-consistent tax scheme to obtain the cooperative solution in the non-cooperative case.
Keywords: differential game, overlapping generations, pollution, Pontryagin's Maximum Principle, Nash equilibrium.
@article{CGTM_2012_5_a27,
     author = {Stefan Wrzaczek and Ekaterina Shevkoplyas and Sergey Kostyunin},
     title = {Differential {Game} of {Pollution} {Control} with {Overlapping} {Generations}},
     journal = {Contributions to game theory and management},
     pages = {310--320},
     publisher = {mathdoc},
     volume = {5},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2012_5_a27/}
}
TY  - JOUR
AU  - Stefan Wrzaczek
AU  - Ekaterina Shevkoplyas
AU  - Sergey Kostyunin
TI  - Differential Game of Pollution Control with Overlapping Generations
JO  - Contributions to game theory and management
PY  - 2012
SP  - 310
EP  - 320
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2012_5_a27/
LA  - en
ID  - CGTM_2012_5_a27
ER  - 
%0 Journal Article
%A Stefan Wrzaczek
%A Ekaterina Shevkoplyas
%A Sergey Kostyunin
%T Differential Game of Pollution Control with Overlapping Generations
%J Contributions to game theory and management
%D 2012
%P 310-320
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2012_5_a27/
%G en
%F CGTM_2012_5_a27
Stefan Wrzaczek; Ekaterina Shevkoplyas; Sergey Kostyunin. Differential Game of Pollution Control with Overlapping Generations. Contributions to game theory and management, Tome 5 (2012), pp. 310-320. http://geodesic.mathdoc.fr/item/CGTM_2012_5_a27/

[1] Anita S., Analysis and control of age-dependent population dynamics, Kluwer Academic Publishers, 2001 | MR | Zbl

[2] Bacchiega E., Lambertini L., Palestini A., “On the time consistency of equilibria in additively separable differential games”, Journal of Optimization Theory and Applications, 145 (2008), 415–427 | DOI | MR

[3] Barro R. J., Becker G. S., “Fertility Choice in a Model of Economic Growth”, Econometrica, 57:2 (1989), 481–501 | DOI | Zbl

[4] Basar T., Olsder G. J., Dynamic Noncooperative Game Theory, Academic Press, 1982 | MR

[5] Breton M., Zaccour G., Zahaf M., “A differential game of joint implementation of environmental projects”, Automatica, 41:10 (2005), 1737–1749 | DOI | MR | Zbl

[6] Brokate M., “Pontryagin's principle for control problems in age-dependent population dynamics”, Journal of Mathematical Biology, 23 (1985), 75–101 | DOI | MR | Zbl

[7] Dockner E., Jørgensen S., Van Long N., Sorger G., Differential Games In Economics and Management Science, Cambridge University Press, 2000 | MR | Zbl

[8] Feichtinger G., Hartl R., Optimale Kontrolle ökonomischer Prozesse. Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften, Walter de Gruyter, 1986 | MR

[9] Feichtinger G., Tragler G., Veliov V. M., “Optimality conditions for age-structured control systems”, Journal of Mathematical Analysis and Applications, 288 (2003), 47–68 | DOI | MR | Zbl

[10] Grass D., Calkins J. P., Feichtinger G., Tragler G., Behrens D., Optimal control of nonlinear processes: With applications in drugs, corruption and terror, Springer, Berlin, 2008 | MR

[11] Grilli L., “Resource extraction activity: an intergenerational approach with asymmetric players”, Game Theory and Applications, 13 (2008), 45–55 | MR

[12] Grilli L., “A Stackelberg differential game with overlapping generations for the management of a renewable resource”, Statistical Science and Interdisciplinary Research, 6 (2009), 221–235 | DOI | MR | Zbl

[13] Jørgensen S., Yeung D. W. K., “Inter- and intragenerational renewable resource extraction”, Annals of Operations Research, 88 (1999), 275–289 | DOI | MR

[14] Jørgensen S., Yeung D. W. K., “Cooperative solution of a game of intergenerational renewable resource extraction”, Game Theory and Applications, 6 (2001), 53-–72 | MR

[15] Jørgensen S., Yeung D. W. K., “An overlapping generations stochastic differential game”, Automatica, 41 (2005), 69–74 | DOI | MR

[16] Shevkoplyas E., Kostyunin S., “Modeling of Environmental projects under condition of a random time horizon”, Contributions to game theory and management, 4, 2011, 447–459 | MR | Zbl