ABSTRACT
Equilibria for discontinuous noncooperative games: applications of
topological measure theory.
Erik Balder
For discontinuous games Simon and Zame introduced a new approach
to the existence of equilibria in discontinuous games, where the usual
fixed point approach breaks down. Their approach is based on a discrete
approximation scheme, based on discrete approximating games, with a
concomitant sequence of approximate mixed Nash equilibria.
The weak limit of this sequence allows an equilibrium interpretation
for the original, discontinuous game via so-called endogenous
sharing rules.
We shall show that in this situation also a very natural continuous
approximation scheme exists, based on continuous approximating
games. Such a scheme produces more precise information about the
equilibrium for the original, discontinuous game. As examples show,
it has also strong computational advantages.
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Martijn Pistorius
(pistorius@math.uu.nl)
Last Updated: February 5, 2002