Sion’s minimax theorem

2021 ◽  
pp. 267-269
Keyword(s):  
Minimax Theorem

MONTE CARLO METHODS IN FUZZY GAME THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 259-269 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Game Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Mixed Strategy ◽  
Minimax Theorem ◽  
Approximate Solutions ◽  
Mixed Strategies ◽  
Fuzzy Game ◽  
Zero Sum

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players [Formula: see text] and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values [Formula: see text] for Player I and [Formula: see text] for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at [Formula: see text] and [Formula: see text] to see if there is a Minimax theorem [Formula: see text] for this fuzzy game.

scholarly journals A saddle point type solution for a system of operator equations

2021 ◽  
pp. 1-12
Author(s):  
Piotr Kowalski
Keyword(s):  
Saddle Point ◽  
Minimax Theorem ◽  
Dirichlet Problems ◽  
Type Solution ◽  
Operator Equations ◽  
Potential Operators ◽  
System Of Operator Equations ◽  
Ky Fan ◽  
Point Type

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.

A note on Ky Fan's minimax theorem

1982 ◽  
Vol 39 (4) ◽  
pp. 401-407 ◽  
Author(s):  
I. Joó ◽  
L. L. Stachó
Keyword(s):  
Minimax Theorem

A two functions, noncompact topological minimax theorem

1996 ◽  
Vol 73 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Cao-Zong Cheng ◽  
Bor-Luh Lin
Keyword(s):  
Minimax Theorem

A minimax theorem in the presence of unbounded Palais-Smale sequences

2009 ◽  
Vol 172 (1) ◽  
pp. 125-143 ◽  
Author(s):  
Jiří Horák ◽  
Marcello Lucia
Keyword(s):  
Minimax Theorem
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