ISSN:
1572-9036
Keywords:
90C31
;
90D10
;
54C60
;
Parametric optimization
;
Nash equilibrium
;
continuous solutions
;
Serre multifunctions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The question of the existence of approximate solutions in parametric optimization is considered. Most results show that (under hypotheses) if a certain optimization problem has an approximate solution x 0 for a value p 0 of a parameter, then an approximate solution x=b(p) can be found for p in P, with b continuous, b(p 0)=x0, and any two such bs are homotopic. Some topological methods (use of fibrations) are used to weaken the usual ‘convex’ hypotheses of such results. An equisemicontinuity condition (relative to a constraint) is introduced to allow some noncompactness. The results are applied to get approximate Nash equilibrium results for games with some nonconvexity in the strategy sets.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00047533
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