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Monitoring cooperative equilibria in a stochastic differential game. (English) Zbl 0830.90143

The objective of this paper is to study a class of equilibria for stochastic differential games which are based on monitoring an implicit cooperative solution. The equilibrium is reached by implementing a random triggering scheme which ranges the mode of play when there is an indication that at least one player may be departing from the cooperative solution.
It is shown that these equilibria can be designed in such away that they generate payoffs which dominate those obtained via the classical feedback Nash equilibrium for the original stochastic diffusion game. The final part of this paper describes the numerical experiments done with the fisheries exploitation model which exhibit the dominance of some cooperative equilibria over the noncooperative feedback Nash equilibrium.

MSC:

91A15 Stochastic games, stochastic differential games
91A23 Differential games (aspects of game theory)
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[1] Porter, R. H.,Optimal Cartel Trigger Strategies, Journal of Economic Theory, Vol. 29, pp. 313–338, 1983. · Zbl 0511.90020
[2] Green, E. J., andPorter, R. H.,Noncooperative Collusion under Imperfect Price Information, Econometrica, Vol. 52, pp. 87–100, 1984. · Zbl 0526.90013
[3] Friedman, J. W.,Oligopoly and the Theory of Games, North-Holland, Amsterdam, Holland, 1977. · Zbl 0385.90001
[4] Haurie, A., andTolwinski, B.,Cooperative Equilibria in Discounted Stochastic Sequential Games, Journal of Optimization Theory and Applications, Vol. 64, pp. 511–535, 1990. · Zbl 0681.90097
[5] Haurie, A.,Piecewise Deterministic and Piecewise Diffusion Differential Games, Decision Processes in Economics, Edited by G. Ricci, Springer-Verlag, Berlin, Germany, 1991. · Zbl 0778.90100
[6] Haurie, A.,From Repeated to Differential Games: How Time and Uncertainty Pervade the Theory of Games (to appear). · Zbl 0816.90143
[7] Kushner, H. J.,Probability Methods for Approximation in Stochastic Control and Elliptic Equations, Academic Press, New York, New York, 1977. · Zbl 0547.93076
[8] Akian, M., andChancellier, J. P.,Dynamic Programming Complexity and Applications, Proceedings of the 27th IEEE Conference on Decision and Control, Austin, Texas, 1988. · Zbl 0682.65077
[9] Clark, C. W.,Restricted Access to Common-Property Resources: A Game Theoretic Analysis, Dynamic Optimization and Mathematical Economics, Edited by P. T. Liu, Plenum Press, New York, New York, 1980. · Zbl 0444.90028
[10] Munro, G. R.,The Optimal Management of Transboundary Renewable Resources, Canadian Journal of Economics, Vol. 12, pp.355–376, 1979.
[11] Hamalainen, R., Haurie, A., andKaitala, V.,Equilibria and Threat in a Fishery Management Game, Optimal Control Applications and Methods, Vol. 6, pp. 315–333, 1985. · Zbl 0631.90017
[12] Selten, R.,Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, Vol. 4, pp. 25–55, 1975. · Zbl 0312.90072
[13] Krylov, N. V.,Controlled Diffusion Processes, Springer-Verlag, Berlin, Germany, 1980. · Zbl 0436.93055
[14] Cournot, A.,Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette, Paris, France, 1838.
[15] Haurie, A., andLeizarowitz, A.,Overtaking Optimal Regulation and Tracking of Piecewise Diffusion Linear Systems, SIAM Journal on Control and Optimization, Vol. 30, pp. 816–837, 1992. · Zbl 0767.93084
[16] Ghosh, M. K., Arapostathis, A., andMarcus, S. I.,Optimal Control of Switching Diffusions with Application to Flexible Manufacturing Systems, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, 1991.
[17] Howard, R. A.,Dynamic Programming and Markov Processes, The MIT Press, Cambridge, Massachusetts, 1960. · Zbl 0091.16001
[18] Breton, M., Filar, J., Haurie, A., andSchultz, T. A.,On the Computation of Equilibria in Discounted Stochastic Games, Dynamic Games and Applications in Economics, Edited by T. Başar, Springer-Verlag, Berlin, Germany, 1986. · Zbl 0597.90099
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