A game theory approach to the Iranian forest industry raw material market

Dynamic game theory is applied to analyze the timber market in northern Iran as a duopsony. The Nash equilibrium and the dynamic properties of the system based on marginal adjustments are determined. When timber is sold, the different mills use mixed strategies to give sealed bids. It is found that the decision probability combination of the different mills follow a special form of attractor and that centers should be expected to appear in unconstrained games. Since the probabilities of different strategies are always found in the interval [۰,۱], the boundaries of the feasible set are sometimes binding constraints. Then, the attractor becomes a constrained probability orbit. In the studied game, the probability that the Nash equilibrium will be reached is almost zero. The dynamic properties of timber prices derived via the duopsony game model are also found in the real empirical price series from the north of Iran.   REFERENCES Aumann, R.J. & Hart, S. (۱۹۹۲) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland ۱, ۷۳۳ p. Aumann, R.J. & Hart, S. (۱۹۹۴) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland ۲, ۷۸۶ p. Aumann, R.J. & Hart, S. (۲۰۰۲) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland ۳, ۸۳۲ p. Bellman, R. (۱۹۵۳) On a new iterative algorithm for finding the solutions of games and linear programming problems. Research Memorandum, The RAND Corporation, Santa Monica, ۴۷۳p. Brown, G.W. & von Neumann, J. (۱۹۵۰) Solution of a game by differential equations. (Eds. H.W. Kuhn & A.W. Tucker). Contributions to the theory of games. Princeton University Press, Annals of Mathematics Studies, ۲۴, ۷۳–۷۹. Carter, D.R. & Newman, D.H. (۱۹۹۸) The impact of reserve prices in sealed bid federal timber sale auctions. Forest Science, ۴۴, ۴۸۵-۴۹۵. Cournot, A.A. (۱۸۳۸) Recherches sur les principes mathe matiques de la theorie des Richesses. M. Riviere and Cie. Paris. Researches into the mathematical principles of wealth (English translation), A. M. Kelly, New York. ۱۹۶۰. Dresher, M. (۱۹۶۱) Games of strategy, theory and applications. Prentice-Hall. Flåm, S.D. (۱۹۹۰) Solving non-cooperative game by continuous subgradient projection methods. (Eds. H.J. Sebastian & K. Tammer) System Modelling and Optimization. Lecture notes in control and information sciences. ۱۴۳, ۱۲۳-۱۵۵. Flåm, S.D. (۱۹۹۶) Approaches to economic equilibrium. Journal of Economic Dynamics and Control. ۲۰, ۱۵۰۵-۱۵۲۲. Flåm, S.D. (۱۹۹۹) Learning equilibrium play: A myopic approach. Computational Optimization and Applications. ۱۴, ۸۷-۱۰۲. Flåm, S.D. (۲۰۰۲) Convexity, differential equations and games. Journal of Convex Analysis. ۹, ۴۲۹-۴۳۸. Flåm, S.D. & Zaccour, G. (۱۹۹۱) Stochastic games, event-adapted equilibria and their Computation. University of Bergen, Department of Economics, Norway. Report ۹۱. Isaacs, R. (۱۹۶۵) Differential games, A mathematical theory with applications to warfare and pursuit, control and optimization. Wiley. ۴۰۸ p. Kalai, E. & M. Smorodinsky. (۱۹۷۵) Other Solutions to Nash's Bargaining Problem. Econometrica. ۴۳, ۵۱۳-۵۱۸. Mohammadi Limaei & Lohmander ۷۱ Koskela, E. & Ollikainen, M. (۱۹۹۸) A gametheoretic model of timber prices with capital stock: an empirical application to the Finnish pulp and paper industry. Canadian Journal of Forest Research. ۲۸, ۱۴۸۱-۱۴۹۳. Lohmander, P. (۱۹۹۴) Expansion dynamics and noncooperative decisions in stochastic markets: Theory and pulp industry application. (Eds. F. Helles & M. Linddal). Scandinavian Forest Economics, Proceedings from the Scandinavian Society of Forest Economics, Denmark, pp. ۱۴۱-۱۵۲. Lohmander, P. (۱۹۹۷) The constrained probability orbit of mixed strategy games with marginal adjustment: General theory and timber market application. System Analysis - Modelling – Simulation, ۲۹, ۲۷-۵۵. Luce, R.D. & H. Raffia. (۱۹۵۷) Games and decisions, introduction and critical survey. Wiley. ۵۰۹pp. Nash, J.F. (۱۹۵۰۰ The bargaining problem, Econometrica, ۱۸, ۱۵۵-۶۲ Neumann, J. & Morgenstern O. (۱۹۴۴) The Theory of Games and Economic Behavior. ۲nd edition. Princeton University Press, ۷۰۴ p. Rasmusen, E. (۱۹۹۰) Games and information, an introduction to game theory. Basil Blackwell, ۴۴۸ p. Robinson, J. (۱۹۵۱) An iterative method of solving a game. Annals of mathematics. ۵۴, ۲۹۶-۳۰۱. Schelling, T. (۱۹۶۰) Strategy of conflict. Harvard University Press,  ۳۰۹ p. Selten, R. (۱۹۷۵) Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory. ۴, ۲۵-۵۵. Von Neumann, J. (۱۹۵۴) A numerical method to determine optimum strategy. Naval Research Logistic Quarterly ۱. Von Neumann, J. & Morgenstern O. (۱۹۴۴) Theory of games and economic behavior. Princeton, ۷۰۴ p. Von Stackelberg, H. (۱۹۳۴) Marketform und gleichgewicht. Wien, Von Stackelberg, H. (۱۹۳۸) Probleme der unvollkommenen konkurens. Weltwirtschaftlisches Arkiv. ۴۸, ۹۵-۱۱۴.

Keywords:

Iranian forest industry , Game Theory , Nash equilibrium , Constrained probability orbit