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Difference between revisions of "Game theory"

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It is a field of [[mathematics]] commonly associated with [[economics]] and [[evolutionary biology]].  Game theory requires interaction between participants and evaluates the possible outcomes of those interactions and what utility each participant receives.  Game theory provides models for behavior in many diverse situations, and is used in many academic fields from [[political science]] to [[computer science]].
 
It is a field of [[mathematics]] commonly associated with [[economics]] and [[evolutionary biology]].  Game theory requires interaction between participants and evaluates the possible outcomes of those interactions and what utility each participant receives.  Game theory provides models for behavior in many diverse situations, and is used in many academic fields from [[political science]] to [[computer science]].
  
==Simple Example:  Prisoner's Dilemma==
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==Simple example:  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.
 
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.
  
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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.
 
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==
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==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.
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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==
 
==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.

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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 actors: that the participants take course that offers them the best outcome reasonably available under the circumstances.

It is a field of mathematics commonly associated with economics and evolutionary biology. Game theory requires interaction between participants and evaluates the possible outcomes of those interactions and what utility each participant receives. Game theory provides models for behavior in many diverse situations, and is used in many academic fields from political science to computer science.

Simple example: 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.