A stochastic version of a Stackelberg-Nash-Cournot equilibrium model

We consider a stochastic version of the Stackelberg-Nash-Cournot model proposed by Murphy et al. (Murphy, F. H., H. D. Sherali, A. L. Soyester. 1983. Stackelberg-Nash-Cournot equilibria characterizations and computations. Oper. Res. 31 253--276.). In the first stage, the leader chooses and announces his production level taking into account the reaction of the followers. The decision of the leader is taken when market demand is uncertain. In the second stage, the followers, knowing the leader's output, react to this level according to the Cournot assumption. At this stage, demand is known. We study the extension of the Murphy et al. model and give a numerical illustration of this model using the European gas market.

[1]  James W. Friedman,et al.  Oligopoly and the theory of games , 1977 .

[2]  Anthony Fiacco.  Continuity of the Optimal Value Function Under the Mangasarian-Fromovitz Constraint Qualification. , 1980 .

[3]  Sanford J. Grossman.  Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs , 1981 .

[4]  Hanif D. Sherali,et al.  A mathematical programming approach for determining oligopolistic market equilibrium , 1982, Math. Program..

[5]  William W. Hogan,et al.  On Convergence of the PIES Algorithm for Computing Equilibria , 1982, Oper. Res..

[6]  European energy report , 1983 .

[7]  Hanif D. Sherali,et al.  Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations , 1983, Oper. Res..

[8]  David S. Abbey,et al.  The effect of market conduct on international steam coal trade , 1984 .

[9]  Simulation of the European gas market up to the year 2000 , 1984 .

[10]  Patrick T. Harker,et al.  A variational inequality approach for the determination of oligopolistic market equilibrium , 1984, Math. Program..

[11]  J. Geanakoplos,et al.  Multimarket Oligopoly: Strategic Substitutes and Complements , 1985, Journal of Political Economy.

[12]  J. Boucher,et al.  Gas trade in the European community during the 1970s: A model analysis , 1985 .

[13]  Harvey J. Greenberg,et al.  Computing Market Equilibria with Price Regulations Using Mathematical Programming , 1985, Oper. Res..

[14]  L. Mathiesen.  Computation of economic equilibria by a sequence of linear complementarity problems , 1985 .

[15]  Lars Mathiesen,et al.  Computational Experience in Solving Equilibrium Models by a Sequence of Linear Complementarity Problems , 1985, Oper. Res..

[16]  C. Kolstad,et al.  Imperfectly Competitive Equilibria in International Commodity Markets , 1986 .

[17]  Economic analysis of natural gas contracts , 1987 .

[18]  C. Bird.  An Optimal Stopping Game in a Restricted Market , 1992 .

[19]  Gül Gürkan,et al.  Sample-path solutions for simulation optimization problems and stochastic variational inequalities , 1997 .