The Environment Protecting Dynamics. An Evolutionary Game Theory approach

Paloma Zapata-Lillo

Contributions to game theory and management, Tome 1 (2007), pp. 539-555.

Résumé

The action of large human conglomerates is behind many of the environmental catastrophes in the last decades. However, these same conglomerates are the main actors in some important environment-protection battles. People might lead to the construction of social organizations, and achieve a kind of accumulation of a protecting stock (laws, protocols, social conscience, etc). Frequently, those social movements grow up and become strong, but they do not remain forever, they often follow a kind of cycle. We study emergence and dynamics of social organizations through the repetition of a game in an evolutionary context. The history of the conflict goes through stages. The reached stochastic stable equilibrium in each stage determines which organization is formed, and which is the accumulated stock in next stage, leading a new game, and new equilibria.

Détail

Keywords: Prisoner Dilemma, Public Good, Organization that Forces cooperation, Organization Game, Strict Nash Equilibria, Learning Dynamics, Myopic People, Sample of Information, Mistakes, Markov Process, Perturbation, Stochastically Stable Equilibria, Accumulation, Learning-Accumulation Dynamics, Depreciation.

Bibliographie

[1] Axelrod R., The Evolution of Cooperation, Basic Books, New York, 1984

[2] Binmore K., Game Theory and the Social Contract, v. 1, Playing Fair, MIT Press, Cambridge–London, 1995 ; v. 2, Just Playing, 1998 | MR

[3] Freidlin M., Wentzell A., Random Perturbations of Dynamical Systems, Springer-Verlag, New York, 1984 | MR | Zbl

[4] Glance N. S., Huberman B. A., “The Outbreak of Cooperation”, Journal of Mathematical Sociology, 17:4 (1993), 281–302 | DOI | Zbl

[5] Glance N. S., Huberman B. A., “Training and Turnover in the Evolution of Organizations”, Organization Science, 8:1 (1997), 84–96 | DOI

[6] Hardin G., “The tragedy of the commons”, Science, 12 (1964), 1243–1248

[7] Kandori M., Mailath G., Rob R., “Learning, Mutation and Long Run Equilibria in Games”, Econometrica, 61 (1993), 29–56 | DOI | MR | Zbl

[8] Kandori M., Rob R., “Evolution of Equilibria in the Long Run: A General Theory and Applications”, Journal of Economic Theory, 65 (1995), 383–414 | DOI | MR | Zbl

[9] Okada A., Sakakibara K., “The Emergence of the State: A Game Theoretic Approach to Theory of Social Contract”, The Economic Studies Quarterly, 42:4 (1991), 315–333

[10] Olson M., The Logic of Collective Action, Harvard University Press, Cambridge, MA, 1965

[11] Ostrom E., Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, Cambridge, 1990

[12] Ostrom E., “A Behavioral Approach to the Rational Choice Theory of Collective Action”, American Political Science Review, 92:1 (1998), 1–22 | DOI

[13] Takayama A., Mathematical Economics, The Dryden Press, Hinsdale, Illinois, 1985 | MR

[14] Weissing F., Ostrom E., “Irrigations and the Games Irrigators Play: Rule Enforcement Without Guards”, Game Equilibrium Models, v. II, Methods, Morals, and Markets, ed. Selten R., Springer-Verlag, Berlin–Heidelberg, 1991, 188–262 | DOI

[15] Young P., “The Evolution of Conventions”, Econometrica, 61 (1993), 57–84 | DOI | MR | Zbl

[16] Young P., Individual Strategy and Social Structure: An Evolutionary Theory of Institutions, Princeton University Press, Princeton, New Jersey, 1998