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InvestmentMAGE
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InvestmentMAGE's Blog : What Does Nash Equilibrium Mean?

Date September 20, 2009    Comments Comments (6)    Rate this post Recommend This Post (117)   
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What Does Nash Equilibrium Mean?
A concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all.

This concept is named after its inventor John Nash and is incorporated in multiple disciplines (ranging from behavioral ecology to economics).

Investopedia explains Nash Equilibrium
If you want to test for a Nash equilibrium, simply reveal each person's strategy to all players. The Nash equilibrium exists if no players change their strategy, despite knowing the actions of their opponents. For example, let's examine a game between Tom and Sam. In this simple game both players can choose: A) received $1, or B) lose $1





Logically, both players choose strategy A and receive a payoff of $1. If you revealed Sam's strategy to Tom and vice versa, you will see that no player deviates from the original choice. Knowing the other player's move means little, and doesn't change behavior. The outcome A,A represents a Nash equilibrium.

Why is this important?

...

You tell me.*

Good Trading,

MAGE


*Hint: See Behavioral Finance.

6 Comment(s):

Author TickerBandit     Date September 20, 2009 23:16 Abuse this post Report Abuse
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Mage,

You are driving at something but not explicitly. Game theory fascinates me but I know little about it really.

Can you be more explicit? I don't own CETV but I noticed you shorted it on Friday. Now for the sake of supposition, let us suppose that I was holding CETV over the weekend and now I have knowledge of your action. This knowledge could have 1 of three effects. I could increase exposure, I could reduce exposure (to include eliminating it), or I could do nothing (the Nash equilibrium state).

How would you interpret each of the trinity of responses?
(Interesting isn't that there is only three viable choices. The same is with your 4-box above. Both players choosing to lose isn't really a viable choice. In logic it is analogous to a set where all outcomes are false. )
Author JoeCole     Date September 21, 2009 04:58  Edited: September 21, 2009 by JoeCole Abuse this post Report Abuse
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It's sort of like the "prisoner's paradox" where two people have the choice of snitching on the other or not snithing. If one snitches and the other does not, the snitcher gets off with no time served and the one who does not snitch gets 10 years. If both snitch on each other then they each get 5 years, and if neither snitches on the other then they both get 6 months. Nash Equilibrium would say that the most logical answer is always to snitch because no matter what the other guy does you get the best outcome, however, this varies in practice based on the number of times the experiment goes on and whether one can punish the other the next time based on previous results or not.

http://en.wikipedia.org/wiki/Prisoner's_dilemma
http://en.wikipedia.org/wiki/Repeated_game
Author InvestmentMAGE     Date September 21, 2009 17:41 Abuse this post Report Abuse
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Hey TB,
Thanks for your questions.
I will expand, watch this space
How would you interpret each of the trinity of responses.
Game theory assumes an interaction between two agents. Either completely competitive (ZERO-SUM GAME) or cooperate / defect (POSITIVE-SUM GAME)
Since there is no interaction in your scenario, I believe its more of an application of probability theory, specifically, Bayes Theorem. Bayes Theorem is a way to update your initial hypothesis (prior probability) in light of new relevant data. Bayes Theorem provides a set of procedures and to perform this calculation.
Although Im quite familiar with Game Theory, Im still learning Bayes Theorem. So let me see if I can work up a decent explanation and get back to you on this.

Cordially,

MAGE
Author InvestmentMAGE     Date September 21, 2009 17:55 Abuse this post Report Abuse
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Hey JC,

Right on. However, Why does Investopedia feel the need to explain it? How is it related to the Stock Market?

Hint: "It's not whether you win or lose, it's how you game the play."

Good Trading,

MAGE
Author InvestmentMAGE     Date September 21, 2009 17:59 Abuse this post Report Abuse
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Author InvestmentMAGE     Date September 28, 2009 14:52 Abuse this post Report Abuse
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Nash Equilibrium:
The reason Nash Equilibrium is important is because we must take other peoples actions into account when we take our actions.
Nash Equilibrium is easily misunderstood.
Both of the above examples are dominate strategies, not Nash Equilibrium.*
A Nash Equilibrium is a mixed-strategy where players choose a probability distribution over possible actions, because NO dominate strategy exits.
The most familiar example in our milieu is the portfolio approach to investing.


MAGE
*I shall endeavor to be more careful in the future.
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