In this chapter, we study various mathematical programming problems in a common framework known as linear complementarity problem. Solving a linear complementarity problem depends on the properties of its underlying matrix class. In this chapter, we discuss matrix theoretic properties of some recent matrix classes encountered in linear complementarity literature and its processability using Lemke’s algorithm.

A Unified Framework for a Class of Mathematical Programming Problems

In this paper, we introduce a generalization of the polymatrix game (a nonzero sum noncooperativen-person game) considered by Howson and relate the problem of computing an equilibrium set of strategies for such a game to the generalized linear complementarity problem of Cottle and Dantzig. For an even more general version of the game we prove the existence of ane-equilibrium set of strategies. We also present a result on the stability of the equilibria based on degree theory.

A Unified Framework for a Class of Mathematical Programming Problems

References

Generalized linear complementarity in a problem ofn-person games

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