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


1 Dept. of Forestry, Faculty of Natural Resources, University of Guilan, Somehe Sara 1144, Iran

2 Dept. of Forest Economics, Faculty of Forest Sciences, Swedish University of Agricultural Sciences (SLU), SE-901 83 Ume?, Sweden.


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 [0,1], 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.
Aumann, R.J. & Hart, S. (1992) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland 1, 733 p.
Aumann, R.J. & Hart, S. (1994) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland 2, 786 p.
Aumann, R.J. & Hart, S. (2002) Handbook of Game Theory with Economic Applications. Amsterdam, North-Holland 3, 832 p.
Bellman, R. (1953) On a new iterative algorithm for finding the solutions of games and linear programming problems. Research Memorandum, The RAND Corporation, Santa Monica, 473p.
Brown, G.W. & von Neumann, J. (1950) 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, 24, 73–79.
Carter, D.R. & Newman, D.H. (1998) The impact of reserve prices in sealed bid federal timber sale auctions. Forest Science, 44, 485-495.
Cournot, A.A. (1838) 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. 1960.
Dresher, M. (1961) Games of strategy, theory and applications. Prentice-Hall. Flåm, S.D. (1990) 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. 143, 123-155.
Flåm, S.D. (1996) Approaches to economic equilibrium. Journal of Economic Dynamics and Control. 20, 1505-1522.
Flåm, S.D. (1999) Learning equilibrium play: A myopic approach. Computational Optimization and Applications. 14, 87-102.
Flåm, S.D. (2002) Convexity, differential equations and games. Journal of Convex Analysis. 9, 429-438.
Flåm, S.D. & Zaccour, G. (1991) Stochastic games, event-adapted equilibria and their Computation. University of Bergen, Department of Economics, Norway. Report 91.
Isaacs, R. (1965) Differential games, A mathematical theory with applications to warfare and pursuit, control and optimization. Wiley. 408 p.
Kalai, E. & M. Smorodinsky. (1975) Other Solutions to Nash's Bargaining Problem. Econometrica. 43, 513-518.
Mohammadi Limaei & Lohmander 71 Koskela, E. & Ollikainen, M. (1998) A gametheoretic model of timber prices with capital stock: an empirical application to the Finnish pulp and paper industry. Canadian Journal of Forest Research. 28, 1481-1493.
Lohmander, P. (1994) 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. 141-152.
Lohmander, P. (1997) The constrained probability orbit of mixed strategy games with marginal adjustment: General theory and timber market application. System Analysis - Modelling – Simulation, 29, 27-55.
Luce, R.D. & H. Raffia. (1957) Games and decisions, introduction and critical survey. Wiley. 509pp. Nash, J.F. (19500 The bargaining problem, Econometrica, 18, 155-62
Neumann, J. & Morgenstern O. (1944) The Theory of Games and Economic Behavior. 2nd edition. Princeton University Press, 704 p.
Rasmusen, E. (1990) Games and information, an introduction to game theory. Basil Blackwell, 448 p.
Robinson, J. (1951) An iterative method of solving a game. Annals of mathematics. 54, 296-301. Schelling, T. (1960) Strategy of conflict. Harvard University Press,  309 p.
Selten, R. (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory. 4, 25-55.
Von Neumann, J. (1954) A numerical method to determine optimum strategy. Naval Research Logistic Quarterly 1.
Von Neumann, J. & Morgenstern O. (1944) Theory of games and economic behavior. Princeton, 704 p.
Von Stackelberg, H. (1934) Marketform und gleichgewicht. Wien, Von Stackelberg, H. (1938) Probleme der unvollkommenen konkurens. Weltwirtschaftlisches Arkiv. 48, 95-114.