Graph continuous function - Revision history

GünniX: Reflist

2025-05-20T04:26:44Z

Reflist

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	==References==		==References==
			{{Reflist}}

	* [[Partha Dasgupta]] and [[Eric Maskin]] 1986. "The existence of equilibrium in discontinuous economic games, I: theory". ''The Review of Economic Studies'', 53(1):1–26		* [[Partha Dasgupta]] and [[Eric Maskin]] 1986. "The existence of equilibrium in discontinuous economic games, I: theory". ''The Review of Economic Studies'', 53(1):1–26

7804j: Rewrite lead

2025-05-14T19:09:49Z

Rewrite lead

← Previous revision		Revision as of 19:09, 14 May 2025
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	{{Short description\|Concept in game theory}}		{{Short description\|Concept in game theory}}
			In [[mathematics]], particularly in [[game theory]] and [[mathematical economics]], a function is '''graph continuous''' if its [[Graph (function)\|graph]]—the set of all input-output pairs—is a closed set in the [[product topology]] of the domain and codomain. In simpler terms, if a sequence of points on the graph converges, its limit point must also belong to the graph. This concept, related to the [[Closed graph theorem\|closed graph property]] in [[functional analysis]], allows for a broader class of discontinuous payoff functions while enabling equilibrium analysis in economic models.
	In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.

			Graph continuity gained prominence through the work of [[Partha Dasgupta]] and [[Eric Maskin]] in their 1986 paper on the existence of equilibria in discontinuous economic games.<ref>{{cite journal \|last1=Dasgupta \|first1=Partha \|last2=Maskin \|first2=Eric \|year=1986 \|title=The Existence of Equilibrium in Discontinuous Economic Games, I: Theory \|journal=The Review of Economic Studies \|volume=53 \|issue=1 \|pages=1–26 \|doi=10.2307/2297588}}</ref> Unlike [[Continuous function\|standard continuity]], which requires small changes in inputs to produce small changes in outputs, graph continuity permits certain well-behaved discontinuities. This property is crucial for establishing equilibria in settings such as [[auction theory]], [[oligopoly]] models, and [[Location theory\|location competition]], where payoff discontinuities naturally arise.

	==Notation and preliminaries==		==Notation and preliminaries==

GhostInTheMachine: Changing short description from "a concept in game theory" to "Concept in game theory"

2023-01-28T22:38:00Z

Changing short description from "a concept in game theory" to "Concept in game theory"

← Previous revision		Revision as of 22:38, 28 January 2023
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	{{Short description\|~~a concept~~ in game theory}}		{{Short description\|Concept in game theory}}
	In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.		In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.

Golden Freddy3124: Changing short description from "a function is graph continuous if it exhibits the following properties" to "a concept in game theory"

2023-01-28T22:14:02Z

Changing short description from "a function is graph continuous if it exhibits the following properties" to "a concept in game theory"

← Previous revision		Revision as of 22:14, 28 January 2023
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	{{Short description\|a ~~function~~ is ~~graph~~ ~~continuous if it exhibits the following properties~~}}		{{Short description\|a concept in game theory}}
	In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.		In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.

Golden Freddy3124: Changing short description from "The study of game theory, a function is graph continuous if it exhibits the following properties" to "a function is graph continuous if it exhibits the following properties"

2023-01-28T22:12:47Z

Changing short description from "The study of game theory, a function is graph continuous if it exhibits the following properties" to "a function is graph continuous if it exhibits the following properties"

← Previous revision		Revision as of 22:12, 28 January 2023
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	{{Short description\|~~The study of game theory,~~ a function is graph continuous if it exhibits the following properties}}		{{Short description\|a function is graph continuous if it exhibits the following properties}}
	In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.		In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.

Golden Freddy3124: Adding short description: "The study of game theory, a function is graph continuous if it exhibits the following properties"

2023-01-28T22:12:20Z

Adding short description: "The study of game theory, a function is graph continuous if it exhibits the following properties"

← Previous revision		Revision as of 22:12, 28 January 2023
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			{{Short description\|The study of game theory, a function is graph continuous if it exhibits the following properties}}
	In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.		In [[mathematics]], and in particular the study of [[game theory]], a [[function (mathematics)\|function]] is '''graph continuous''' if it exhibits the following properties. The concept was originally defined by [[Partha Dasgupta]] and [[Eric Maskin]] in 1986 and is a version of [[continuous function\|continuity]] that finds application in the study of [[continuous game]]s.

JJMC89 bot III: Moving :Category:Continuous mappings to :Category:Theory of continuous functions per Wikipedia:Categories for discussion/Log/2022 December 6#Category:Continuous mappings

2022-12-15T22:18:20Z

Moving Category:Continuous mappings to Category:Theory of continuous functions per Wikipedia:Categories for discussion/Log/2022 December 6#Category:Continuous mappings

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	{{DEFAULTSORT:Graph Continuous Function}}		{{DEFAULTSORT:Graph Continuous Function}}
	[[Category:Game theory]]		[[Category:Game theory]]
	[[Category:~~Continuous~~ ~~mappings~~]]		[[Category:Theory of continuous functions]]

Michael Hardy at 19:37, 3 October 2019

2019-10-03T19:37:07Z

← Previous revision		Revision as of 19:37, 3 October 2019
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	==References==		==References==

	* [[Partha Dasgupta]] and [[Eric Maskin]] 1986. ''The existence of equilibrium in discontinuous economic games, I: theory''. The Review of Economic Studies, 53(1):~~1-26~~		* [[Partha Dasgupta]] and [[Eric Maskin]] 1986. "The existence of equilibrium in discontinuous economic games, I: theory". ''The Review of Economic Studies'', 53(1):1–26

	{{DEFAULTSORT:Graph Continuous Function}}		{{DEFAULTSORT:Graph Continuous Function}}

Erel Segal: added Category:Continuous mappings using HotCat

2019-10-01T18:58:00Z

added Category:Continuous mappings using HotCat

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	{{DEFAULTSORT:Graph Continuous Function}}		{{DEFAULTSORT:Graph Continuous Function}}
	[[Category:Game theory]]		[[Category:Game theory]]
			[[Category:Continuous mappings]]

Erel Segal: Undid revision 452943820 by Lil Abi (talk)

2019-10-01T18:56:07Z

Undid revision 452943820 by Lil Abi (talk)

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	A '''game''' is defined as <math>[(A_i,U_i); i=1,\ldots,N]</math>.		A '''game''' is defined as <math>[(A_i,U_i); i=1,\ldots,N]</math>.
	If a graph is continuous you should connect it if it's not then don't connect it.

	==Definition==		==Definition==