Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations

Article Abstract:

The supply side of an oligopolistic market supplying a homogeneous product noncooperatively is modeled. In this market, there is one leader and N followers. The followers operate under the Cournot assumption of zero conjectural variation and are accordingly called Cournot firms. The leader, called a Stackelberg firm, specifically takes into account the reaction of the Cournot firms to its output. For this situation, the behavior and implications of the joint Cournot reaction curve as generated by plausible economic assumptions are studied. The existence and uniqueness of a Stackelberg-Nash-Cournot equilibrium is studied. An efficient algorithm to determine a set of equilibrating output quantities for the firms is prescribed.

Algorithms, Market research, Algorithm, Market Analysis, Models, Market, Marketing Research

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On Generating Cutting Planes from Combinatorial Disjunctions

Article Abstract:

The solution of multiple choice constrained programs or generalized lattice point problems may be achieved using cutting planes. The present paper presents a method for generating valid cutting planes that are based on combinatorial disjunctions requiring that at least p out of q (q less than or equal to p) constraints be satisfied. Existing methods are subsumed by this technique, which provides a framework for generating cutting planes based on these disjunctions.

Integer programming, Optimization theory, Applications, Programs, Methods, Combinatorics

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A Class of Stochastic Mathematical Programs With Correlated Scale Parameters in the Objective Right-Hand Side

Article Abstract:

A special type of uncertainty with a class of mathematical programming problems is studied. Linear programs are part of the class. The class has scale parameters in the objective function and right-hand side. These parameters are a pair of jointly distributed random variables. A bias is developed when random variables are replaced by their expected values.

Linear programming, Scientific Research, Stochastic Model, Mathematical programming

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