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A fixed point theorem for discontinuous functions

Herings, Peter Jean-Jacques; Laan, Gerard van der; … - 2004

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

Persistent link: https://www.econbiz.de/10011342557

Perfection and stability of stationary points with applications to noncooperative games

Laan, Gerard van der; Talman, Dolf; Yang, Zaifu - 2002

well known refinements of the Nash equilibrium, namely, perfect Nash equilibrium and proper Nash equilibrium, are special … Nash equilibrium is shown to exist for every game. In symmetric bimatrix games, our results imply the existence of a … symmetric proper equilibrium. Applying our results to the field of evolutionary game theory yields a refinement of the …

Persistent link: https://www.econbiz.de/10011327822

Computing integral solutions of complementarity problems

Laan, Gerard van der; Talman, Dolf; Yang, Zaifu - 2004

In this paper an algorithm is proposed to find an integral solution of (nonlinear) complementarity problems. The algorithm starts with a nonnegative integral point and generates a unique sequence of adjacent integral simplices of varying dimension. Conditions are stated under which the algorithm...

Persistent link: https://www.econbiz.de/10011343323

Quantity constrained equilibria

Herings, Peter Jean-Jacques; Laan, Gerard van der; … - 2001

In a standard general equilibrium model it is assumed that there are no price restictionsand that prices adjust … infinitely fast to their equilibrium values. In this paper the set ofadmissible prices is allowed to be an arbitrary convex set …. For such an arbitrary set it cannotbe guaranteed that there exists a constrained equilibrium satisfying the usual …

Persistent link: https://www.econbiz.de/10011325664