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.

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

scholarly journals Common fixed point theorems under an implicit contractive condition on metric spaces endowed with an arbitrary binary relation and an application

2019 ◽  
pp. 2050146
Author(s):  
Md Ahmadullah ◽  
Mohammad Imdad ◽  
Mohammad Arif
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Binary Relation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Common Fixed Point Theorems

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well-known contraction conditions in one go besides yielding several new ones. We also provide an example to demonstrate the generality of our results over several well-known corresponding results of the existing literature. Finally, we utilize our results to prove an existence theorem for ensuring the solution of an integral equation.

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 Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Reny George ◽  
Hemanth Kumar Pathak
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
The Other ◽  
Inclusion Problem ◽  
Integral Inclusion ◽  
New Variant ◽  
Multivalued Contractions ◽  
Filippov Type

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

scholarly journals Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Xingchang Li
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Noncooperative Games ◽  
Generalized Nash Equilibrium ◽  
Common Condition ◽  
Incomplete Preference ◽  
Zorn Lemma

To prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set, we translate the incomplete preference problems into the partial order problems. Using the famous Zorn lemma, we get the existence theorems of fixed point for noncontinuous operators in incomplete preference sets. These new fixed point theorems provide a new way to break through the limitation. Finally, the existence of generalized Nash equilibrium is strictly proved in the n-person noncooperative games under incomplete preference.

scholarly journals Multivalued F-contractions and related fixed point theorems with an application

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3779-3793 ◽  
Author(s):  
Muhammad Ali ◽  
Tayyab Kamran
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Multivalued Mappings

In this paper, we introduce the notions of ?-F-contractions, by combining the notions of ?-?-contraction and F-contraction. Using our new notions we obtain some fixed point theorems for multivalued mappings. As an application we establish an existence theorem for integral equations. An example is also constructed to show an importance of our results.

The existence theorem of a new multi-valued mapping in metric space endowed with graph

2017 ◽  
Vol 33 (2) ◽  
pp. 191-198
Author(s):  
ARAYA KHEAWBORISUT ◽  
◽  
SUTHEP SUANTAI ◽  
ATID KANGTUNYAKARN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Directed Graph ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Ordered Metric Spaces ◽  
New Type

In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.

scholarly journals Some Fixed Point Theorems in -Metric Space Endowed with Graph

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Maria Samreen ◽  
Tayyab Kamran ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contraction Mappings ◽  
Cyclic Operators

We define some notions of contraction mappings in -metric space endowed with a graph and subsequently establish some fixed point results for such classes of contractions. According to the applications of our results, we obtain fixed point theorems for cyclic operators and an existence theorem for the solution of an integral equation.

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