Minimax: Existence and Stability

Hoang Tuy ()
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Hoang Tuy: Institute of Mathematics

A chapter in Pareto Optimality, Game Theory And Equilibria, 2008, pp 3-21 from Springer

Abstract: A unified framework is presented for studying existence and stability conditions for minimax of quasiconvex quasiconcave functions. These theorems include as special cases refinements of several known results from game theory, optimization, and nonlinear analysis. In particular, existence conditions are developed that turn out to be sufficient also for the continuity of the saddle value and stability of the saddle point under continuous perturbation. Also, a lopsided minimax theorem is established that yields as immediate corollaries both von Neumann's classic minimax theorem and Nash's theorem on noncooperative equilibrium.

Keywords: minimax theorems; quasiconvex quasiconcave functions; saddle value; existence conditions; stability conditions; lopsided minimax; cooperative equilibrium (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-77247-9_1

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DOI: 10.1007/978-0-387-77247-9_1

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