# pure-nash - Game Theory Jeffrey Ely Jeffrey Ely Game Theory...

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Game Theory Jeffrey Ely April 19, 2016 Jeffrey Ely Game Theory

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A Beautiful Mind Princeton Mathematicians at a Bar Jeffrey Ely Game Theory
The Four Brunettes and a Blonde Game Four players (Nash and his chums.) Each has the same set of actions A i = { b 1 , b 2 , b 3 , B } . Payoffs π i ( a )= Zero if i chooses the same action as some other player j . And if no other player chooses the same action as i then 1 if i chose b 1 , b 2 , or b 3 . 10 if i chose B . Jeffrey Ely Game Theory

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The 4b1B Game Has no Dominated Strategies Choosing a i = b 1 is not dominated. Take any other action z . If a - i =( z , B , b 2 ) then a i = b 1 gives a payoff of 1. and z would get a payoff of 0. Thus, for any other action z , there is an a - i such that b 1 does better than z . So no z can dominate a i = b 1 . Similarly no other action a i is dominated. Jeffrey Ely Game Theory
So What Should We Predict? Jeffrey Ely Game Theory

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Nash’s Theory One way to understand Nash’s theory is to imagine the players talking before deciding what to do. There are two issues to resolve by planning in advance. Whatever agreement they reach must be credible. There is a conflict of interest. While talk might be of some help in resolving these problems, talk is limited by the fact that each player is ultimately looking out for himself. He is trying to maximize π i . Jeffrey Ely Game Theory
Credible Agreements After all the talking is done, its time to take action.

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