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.
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Tuy, H. (2008). Minimax: Existence and Stability. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_1
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