Browder type fixed point theorems and Nash equilibria in generalized games

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Jiuqiang Liu ◽  
Mingyu Wang ◽  
Yi Yuan
Keyword(s):  
Fixed Point ◽  
Nash Equilibria ◽  
Fixed Point Theorems ◽  
Generalized Games

Fixed point theorems and their applications to theory of Nash equilibria

2006 ◽  
Vol 64 (7) ◽  
pp. 1415-1436 ◽  
Author(s):  
S. Heikkilä ◽  
K. Reffett
Keyword(s):  
Fixed Point ◽  
Nash Equilibria ◽  
Fixed Point Theorems

Extended Nash Equilibria of Nonmonetized Noncooperative Games on Preordered Sets

2015 ◽  
Vol 17 (01) ◽  
pp. 1540009
Author(s):  
Jinlu Li
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Nash Equilibria ◽  
Fixed Point Theorems ◽  
Noncooperative Games ◽  
Noncooperative Game ◽  
Preordered Sets

A noncooperative game is said to be nonmonetized if the ranges of the utilities (payoffs) of the players are preordered sets. In this paper, we examine some nonmonetized noncooperative games in which both of the collection of strategies and the ranges of the utilities for the players are preordered sets. Then, we spread the concept of extended Nash equilibria of noncooperative games from posets to preordered sets. By applying some fixed point theorems on preordered sets and by using the order preserving property of the utilities, we prove an existence theorem of extended Nash equilibria for nonmonetized noncooperative games.

On the existence of ɛ-fixed points

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Tiziana Cardinali
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nash Equilibria ◽  
Fixed Point Theorems ◽  
Broad Sense ◽  
Approximate Fixed Point

AbstractIn this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.

scholarly journals Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yan-Mei Du
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Recent Literature ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Abstract Convex Space ◽  
Generalized Games ◽  
Set Valued Mappings ◽  
Qualitative Games

We firstly prove some new fixed point theorems for set-valued mappings in noncompact abstract convex space. Next, two existence theorems of maximal elements for class of𝒜C,θmapping and𝒜C,θ-majorized mapping are obtained. As in applications, we establish new equilibria existence theorems for qualitative games and generalized games. Our theorems improve and generalize the most known results in recent literature.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

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