Game theory: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Shamira Gelbman
(von neumann)
mNo edit summary
 
(6 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{subpages}}
{{subpages}}
'''Game theory''' is the study of strategy and decision-making. It divides competition into '''games of skill''', '''games of chance''' and '''games of strategy'''.  Most discussions in game theory focus on the games of strategy, which also have an assumption of [[rational actor]]s: that the participants take course that offers them the best outcome reasonably available under the circumstances.
'''Game theory''' is the mathematical study of strategy and decision-making. Most discussions in game theory focus on [[game of strategy|games of strategy]] that assume [[rational actor]]s: that is, that the participants take the course that offers them the best outcome reasonably available under the circumstances.


Game theory is a field of [[mathematics]] that is often applied to the subject matter of other disciplines, including [[economics]], [[political science]], [[computer science]], and [[evolutionary biology]]. It provides models for behavior in diverse situations by modeling interactions among participants and evaluating the possible outcomes of those interactions and what utility each participant receives.
Although game theory is a field of [[mathematics]], it is often applied to the subject matter of other disciplines, most notably [[economics]], but also many others including [[political science]], [[computer science]], and [[evolutionary biology]]. It provides models for behavior in diverse situations by modeling interactions among participants and evaluating the possible outcomes of those interactions and what utility each participant receives.


==History of game theory==
==History of game theory==


The development of game theory as a distinct subfield of mathematics is attributed to [[John Von Neumann]], a Hungarian-born mathematician who began publishing papers on the theory of games in 1928. In 1944, he and [[Oskar Morgenstern]] published ''Theory of Games and Economic Behavior.''  
The development of game theory as a distinct field within mathematics is attributed to [[John von Neumann]], a Hungarian-born mathematician who began publishing papers on the theory of games in 1928. In 1944, he and [[Oskar Morgenstern]] published ''Theory of Games and Economic Behavior'', a book that is credited as the ground-breaking work of the field.
 
==Types of Games==


==Simple example: The prisoner's dilemma==
==Simple example: The prisoner's dilemma==
Line 20: Line 22:


==Iterated Games==
==Iterated Games==
While some games are only played once, others are played multiple times consecutively.  This introduces the history into the decision-making logic  In the above Prisoner's Dilemma example, knowing whether your partner was faithful or not previously might have an impact on a player's decision.
While some games are only played once, others are played multiple times consecutively.  This introduces the history into the decision-making logic  In the above Prisoner's Dilemma example, knowing whether your partner was faithful or not previously might have an impact on a player's decision.[[Category:Suggestion Bot Tag]]

Latest revision as of 06:01, 20 August 2024

This article is developing and not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

Game theory is the mathematical study of strategy and decision-making. Most discussions in game theory focus on games of strategy that assume rational actors: that is, that the participants take the course that offers them the best outcome reasonably available under the circumstances.

Although game theory is a field of mathematics, it is often applied to the subject matter of other disciplines, most notably economics, but also many others including political science, computer science, and evolutionary biology. It provides models for behavior in diverse situations by modeling interactions among participants and evaluating the possible outcomes of those interactions and what utility each participant receives.

History of game theory

The development of game theory as a distinct field within mathematics is attributed to John von Neumann, a Hungarian-born mathematician who began publishing papers on the theory of games in 1928. In 1944, he and Oskar Morgenstern published Theory of Games and Economic Behavior, a book that is credited as the ground-breaking work of the field.

Types of Games

Simple example: The prisoner's dilemma

A case study in game theory is perhaps the best-known example: The Prisoner's Dilemma. Two prisoners are being interrogated separately, suspected as accomplices for the same crime. If neither confesses, they face only a short sentence of length A. If one betrays the other, that prisoner goes free while the other prisoner gets a very lengthy sentence (B). If both betray their partner, they both get a medium-long sentence (C). Sentence A < C <B.

The outcome with the least prison time is one of dual-silence. However, since each individual patient is better served by going free (as opposed to serving sentence A), and would rather serve sentence C than B (if the partner betrays them), it makes the most sense for each individual prisoner to betray, regardless of the action of their accomplice.

Symmetry

In the above example of the Prisoner's Dilemma, both players have exactly the same choices and the same outcomes. Games like this are said to be symmetric, as the roles each player plays are identical. In other games, each player's role is different. For instance, one player might make an offer, which the other player either accepts or rejects. These games are asymmetric.

Zero-sum games

A zero-sum game is one in which one player can only benefit at the equal detriment of the other. In this case, the gains and harms in each decision add up to zero.

Iterated Games

While some games are only played once, others are played multiple times consecutively. This introduces the history into the decision-making logic In the above Prisoner's Dilemma example, knowing whether your partner was faithful or not previously might have an impact on a player's decision.