Cooperation in Bioresource Management Problems
Abstract
This paper is devoted to overview of the previously available and the author's own results of cooperative behavior analysis in dynamic games related to bioresource management problems. The methodological schemes to maintain the cooperation are considered and modified. The incentive condition for rational behavior and characteristic function construction method are presented. The question of coalition stability is revised and extended. The cooperative behavior determination schemes for games with asymmetric players are obtained. Some analytical and numerical modelling results for particular dynamic bioresource management problems are presented.
Keywords:
dynamic games, bioresource management problem, Nash equilibrium, cooperative equilibrium, incentive equilibrium, dynamic stability, imputation distribution procedure, incentive conditions for rational behavior, coalition stability, asymmetric players, different planning horizons
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References
Abakumov, A. I. (1994). Optimal harvesting in populations’ models. Applied and indastrial mathematics review, 1(6), 834–849 (in Russian).
Abakumov, A. I. (1993). Control and optimization in the harvesting models. Vladivostok: Dalnauka (in Russian).
Baturin, V.A., Skitnevskii, D.M. and Cherkashin, A.K. (1984). Planning and forecast for ecological-economical systems. Novosibirsk: Nauka (in Russian).
Barrett, S. (1994). Self-enforcing International Environmental Agreements. Oxford Economic Papers, 46, 878–894.
Bazikin, A.D. (1985). Mathematical biophisics of interacting populations. Moscow: Nauka.
Berdnikov, S.V., Vasilchenko, V.V. and Selutin, V.V. (1999). Mathematical modeling of exogenous perturbation in trophic networks. Applied and indastrial mathematics review, 6(2), 145–158 (in Russian).
Bloch, F. (1995). Sequential formation of coalitions with fixed payoff division and externalities. Games Econ. Behav., 14, 90–123.
Bloch, F. (1996). Noncooperative models of coalition formation in games with spillovers. In: Carraro C., Siniscalco D. eds. New Direction in Economic Theory of Environment. Cambridge: Cambridge University Press.
Breton, M. and Keoula, M.Y. (2014) A great fish war model with asymmetric players. Ecological Economics, 97, 209–223.
Carraro, C. (1997) The structure of International Environmental Agreements. Paper presented at the FEEM/IPCC/Stanford EMF Conference on ”International Environmental Agreements on Climate Change”. Venice, pp. 309–328.
Carraro, C. The economics of coalition formation. In: Gupta J., Grubb M. eds. Climate Change and European Leadership. Kluwer Academic Publishers, 2000. pp. 135–156.
Carraro, C. and Siniscalco, D. (1992) The international protection of the environment. J. Publ. Econ., 52, 309–328.
Chaudhuri, K. (1986) A bioeconomic model of harvesting a multispecies fishery. Ecological Modelling, 32, 267–279.
Clark, C.W. (1985). Bioeconomic modelling and fisheries management. NY: Wiley.
D’Aspremont, C., Jacquemin, A., Gabszewicz, J.J. and Weymark, J.A. (1983). On the stability of collusive price leadership. Can. J. Econ., 16(1), 17–25.
De Zeeuw, A. (2008). Dynamic effects on stability of International Environmental Agreements. J. of Environmental Economics and Management, 55, 163–174.
Ehtamo, H. and Hamalainen, R.P. (1993). A cooperative incentive equilibrium for a resource management problem. J. of Economic Dynamics and Control, 17, 659–678.
Eyckmans, J. and Finus, M. (2003). Coalition formation in a global warming game: how the design of protocols affects the success of environmental treaty-making. Working paper 56, CLIMNEG 2.
Finus, M. (2008). Game theoretic research on the design of International Environmental Agreements: insights, critical remarks and future challenges. Int. Rev. of Environmental and Resource Economics, 2, 29–67.
Finus, M. and Rundshagen, B. (2003). Endogenous coalition formation in global pollution control: a partition function approach. In: Carraro C. ed. Endogenous formation of economic coalitions. Cheltenham: Edward Elgar, pp. 199–243.
Fisher, R.D. and Mirman, L. J. (1992). Strategic dynamic interactions: fish wars. J. of Economic Dynamics and Control, 16, 267–287.
Fisher, R.D. and Mirman, L. J. (1996). The complete fish wars: biological and dynamic interactions. J. of Env. Econ. and Manag., 30, 34–42.
Gimelfard, A.A., Ginzburg, L.R., Poluektov, R.A., Puh, Yu.A. and Ratner, V.A. (1974). Dynamic theory of biological populations. Moscow: Nauka (in Russian).
Goh, B. S. (1980). Management and analysis of biological populations. Agricultural and Managed-Forest Ecology. Amsterdam: Elsevier.
Gromova, E.V. and Petrosyan, L.A. (2015) On a approach to the construction of characteristic function for cooperative differential games. Math. Game Theory and Appl., 7(4), 19–39 (in Russian).
Gurman, V. I. and Druzhinina, I.P. (1978). Nature system models. Novosibirsk: Nauka (in Russian).
Hamalainen, R.P., Kaitala, V. and Haurie, A. (1984). Bargaining on whales: A differential game model with Pareto optimal equilibria. Oper. Res. Letters, 3(1), 5–11.
Haurie, A. (1976). A note on nonzero-sum differential games with bargaining solutions. J. of Opt. Theory and Appl. 18, 31–39.
Haurie, A. and Tolwinski, B. (1984). Acceptable equilibria in dynamic games. Large Scale Systems, 6, 73–89.
Il’ichev, V.G., Rohlin, D.B. and Ougolnitskii, G.A. (2000). About economical mechanisms of bioresource management control. Russian Academy of Sciences belluten. Theory and system control, 4, 104–110 (in Russian).
Ioannidis, A., Papandreou, A. and Sartzetakis E. (2000). International Environmental Agreements: a literature review. Working Papers, GREEN.
Kaitala, V.T. and Lindroos, M. (2007). Game-theoretic applications to fisheries. In: Handbook of operations research in natural resources, pp. 201–215. Springer.
Kulmala, S., Levontin, P., Lindroos, M. and Pintassilgo, P. (2009). Atlantic salmon fishery in the Baltic Sea - A case of trivial cooperation. In ”Essays on the Bioeconomics of the Northern Baltic Fisheries”. Soile Kulmala. PhD thesis, University of Helsinki.
Levhari, D. and Mirman, L. J. (1980). The great fish war: an example using a dynamic Cournot-Nash solution. The Bell J. of Economics, 11(1), 322–334.
Lindroos, M., Kaitala V.T. and Kronbak L.G. (2007). Coalition games in fishery economics. In: Advances in Fishery Economics, pp. 184–195. Blackwell Publishing.
Lindroos, M. (2008). Coalitions in International Fisheries Management. Natural Resource Modeling, 21, 366–384.
Marin-Solano, J. and Shevkoplyas E.V. (2011). Non-constant discounting and differential games with random time horizon. Automatica, 47, 2626–2638.
Mazalov, V.V. and Rettieva, A.N. (2015). Asymmetry in a cooperative bioresource management problem. In: Game-Theoretic Models in Mathematical Ecology. Nova Science Publishers, pp. 113–152.
Mazalov, V.V. and Rettieva, A.N. (2014). Game-theoretic models for cooperative bioresource management problem. In: Models and Methods in the Problem of Interaction between Atmosphere and Hydrosphere: Textbook. Tomsk, pp. 449–489.
Mazalov, V.V. and Rettieva, A.N. (2012). Cooperation maintenance in fishery problems. In: Fishery Management. Nova Science Publishers, pp. 151–198.
Mazalov, V.V. and Rettieva, A.N. (2011). The discrete-time bioresource sharing model. J. Appl. Math. Mech., 75 (2), 180–188.
Mazalov, V.V. and Rettieva, A.N. (2010). Fish wars and cooperation maintenance. Ecological Modelling, 221, 1545–1553.
Mazalov, V.V. and Rettieva, A.N. (2010). Incentive conditions for rational behavior in discrete-time bioresource management problem. Doklady Mathematics 81(3), 399–402.
Mazalov, V.V. and Rettieva, A.N. (2010). Incentive equilibrium in bioresource sharing problem. Journal of Computer and Systems Sciences International, 49(4), 598–606.
Mazalov, V.V. and Rettieva, A.N. (2010). Fish wars with many players. Int. Game Theory Rev., 12(4), 385–405.
Mazalov, V.V. and Rettieva, A.N. (2009). The compleat fish wars with changing area for fishery. IFAC Proceedings Volumes (IFAC – PapersOnLine), 7(1), 168–172.
Mazalov, V.V. and Rettieva, A.N. (2008). Incentive equilibrium in discrete-time bioresource sharing model. Doklady Mathematics, 78(3), 953–955.
Mazalov, V.V. and Rettieva, A.N. (2008). Bioresource management problem with changing area for fishery. Game Theory and Applications, 13, 101–110.
Mazalov, V.V. and Rettieva, A.N. (2008). Incentive equilibrium in bioresource management problem. In: Evolutionary and deterministic methods for design, optimization and control, P. Neittaanmaki, J. Periaux and T. Tuovinen (Eds.). CIMNE. Barcelona. Spain, 451–456.
Mazalov, V.V. and Rettieva, A.N. (2007). Cooperative incentive equilibrium for a bioresource management problem. Contributions to Game Theory and Management, 1, 316–325.
Mo, J. and Walrand, J. (2000). Fair End-to-End Window-Based Congestion Control. IEE/ACM Transactions on Networking, 8(5), 556–567.
Munro, G.R. (1979). The optimal management of transboundary renewable resources. Can. J. of Econ., 12(8), 355–376.
Munro, G.R. (2000). On the Economics of Shared Fishery Resources. In: Int. Relations and the Common Fisheries Policy. Portsmouth, pp. 149–167.
Neumann, J. and Morgenstern, O. (1953). Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Osborn, D.K. (1976). Cartel problems. American Economic Review, 66, 835–844.
Osmani, D. and Tol, R. S. J. (2010). The Case of Two Self-enforcing International Agreements for Environmental Protection with Asymmetric Countries. Computational Economics, 36(2), 93–119.
Ostrom, E. (1990). Governing the commons: the evolution of institutions for collective action. Cambridge University Press.
Owen, G. (1968). Game theory. NY: Academic Press.
Petrosjan, L.A. (1993). Differential game of pursuit. World Scientific, Singapore.
Petrosjan, L.A. and Zaccour, G. (2003). Time-consistent Shapley value allocation of pollution cost reduction. J. of Econ. Dyn and Contr., 27(3), 381–398.
Petrosjan, L.A. and Zenkevich, N.A. (1996). Game theory. World Scientific, Singapore.
Petrosyan, L.A. (1997). Stability of differential games with many players’ solutions. Vestnik of Leningrad university, 19, 46–52 (in Russian).
Petrosyan, L.A. and Danilov, N.N. (1979). Stability of nonantogonostic differential games with transferable payoffs’ solutions. Vestnik of Leningrad university, 1, 52–59 (in Russian).
Petrosyan, L.A. and Danilov, N.N. (1985). Coopeartive differential games and applications. Tomsk (in Russian).
Petrosyan, L.A. and Zakharov, V.V. (1981). Game-theoretic approach to nature protect problem. Vestnik of Leningrad university, 1, 26–32 (in Russian).
Petrosyan, L.A. and Zakharov, V.V. (1997). Mathematical models in ecology. SPb: SPb State University (in Russian).
Petrosyan, L.A. and Zakharov, V.V. (1986). Introduction to mathematical ecology. Leningrad: Lenigrad State University (in Russian).
Pintassilgo, P. and Lindroos, M. (2008). Coalition formation in straddling stock fisheries: a partition function approach. Int. Game Theory Rev., 1, 303–317.
Plourde, C.G. and Yeung, D. (1989). Harvesting of a transboundary replenishable fish stock: a noncooperative game solution. Marine Resource Economics, 6, 57–70.
Puh, Yu.A. (1983). Equilibrium and stability in populaitons dynamic models. Moscow: Nauka.
Ray, D. and Vohra, R. (1997). Equilibrium binding agreements. Jour. of Econ. Theory, 73, 30–78.
Rettieva, A.N. (2017). Equilibria in dynamic multicriteria games. Int. Game Theory Rev., 19(1), 1750002.
Rettieva, A.N. (2014). A bioresource management problem with different planning horizons. Automation and Remote Control, 76(5), 919–934.
Rettieva, A.N. (2014). A discrete-time bioresource management problem with asymmetric players. Automation and Remote Control, 75(9), 1665–1676.
Rettieva, A.N. (2013). Bioresource management problem with asymmetric players. Computational information technologies for environmental sciences: selected and reviewed papers presented at the International conference CITES-2013, 127–131.
Rettieva, A.N. (2012). Stable coalition structure in bioresource management problem. Ecological Modelling 235-236, 102–118.
Rettieva, A.N. (2012). A discrete-time bioresource management problem with asymmetric players. Math. Game Theory and Appl., 4(4), 63–72 (in Russian).
Rettieva, A.N. (2011). Fish wars with changing area for fishery. Advances in Dynamic Games. Theory, Applications, and Numerical Methods for Differential and Stochastic Games, 11, 553–563.
Rettieva, A.N. (2011). Coalition structure stability in discrete time bioresource management problem. Math. Game Theory and Appl., 3(3), 39–66 (in Russian).
Rettieva, A.N. (2010). Cooperative bioresource management regulation. Appl. and Indust. Math. Rev., 17(5), 663–672 (in Russian).
Rettieva, A.N. (2009). Cooperative incentive condition in bioresource sharing problem. Large-scale Systems Control, 26.1, 366–384 (in Russian).
Silvert,Wand Smith,W.R. (1977). Optimal exploitation of multispecies community. Math. Biosci., 33, 121–134.
Shapiro, A.P. (1979). Modeling of biological systems. Vladivostok (in Russian).
Shevkoplyas, E.V. (2011). The Shapley value in cooperative differential games with random duration. Annals of the Int. Soc. of Dynamic Games, 11 , 359–373.
Smith, M.J. (1968). Mathematical Ideas in Biology. Cambridge University Press.
Sorger, G. (2006). Recursive Nash bargaining over a productive assert. J. of Economic Dynamics & Control, 30, 2637–2659.
Svirezhev, Yu.M. and Elizarov, E.Ya. (1972). Mathematical modeling of biological systems. Moscow: Nauka (in Russian).
Tolwinski, B., Haurie, A. and Leitmann, G. (1986). Cooperative equilibria in differential games. J. of Math. Anal. and Appl., 119, 182–202.
Vislie, J. (1987). On the optimal management of transboundary renewable resources: a comment on Munro’s paper. Can. J. of Econ., 20, 870–875.
Yeung, D.W.K. (2006). An irrational-behavior-proof condition in cooperative differential games. Int. Game Theory Review, 8(4), 739–744.
Yi, S. S. (1997). Stable coalition structures with externalities. Games and Economic Behavior, 20, 201–237.
Yi, S. S. and Shin, H. (1995). Endogenous formation of coalitions in oligopoly. Mimeo; Department of Economics, Dartmouth College.
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Published
2022-04-16
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Rettieva, A. N. (2022). Cooperation in Bioresource Management Problems. Contributions to Game Theory and Management, 10. Retrieved from https://gametheory.spbu.ru/article/view/13293
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Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
