Dominant Vs Nash Nash Equilibrium for Prisoner's Dilemma Game .At a dominant strategy equilibrium, Peter every player will not change his position any more. Confess Do not At a Nash Equilibrium,every player will not Confess change his position provided that the others Confess 5,5 0,10 do not change their positions. John .Therefore,a dominant strategy Do not 10,0 Confess 2,2 equilibrium must be a Nash equilibrium. What is a mixed What is not a Nash equilibrium? Nash equilibrium? .In the bar scene,Nash suggested everyone should go for his second .To understand what a mixed Nash choice. equilibrium is,let's play the following .This is not a Nash equilibrium because if three person game. you know all the others are going to choose their second choices,then you will certainly change your choice to the most beautiful girl. A three-person game ·Each one can show either one finger or Exercise two fingers. ·If you are the only one showing one Does this game have any finger,then you get dominant strategy equilibrium one dollar from me. If you are the only How many possible outcomes for one showing two this game?How many of them are fingers,then you get Nash equilibria?List all of them. two dollars. Otherwise,everyone gets nothing Can you find the Nash equilibria for this game 1010 Dominant Vs Nash „ At a dominant strategy equilibrium, every player will not change his position any more. „ At a Nash Equilibrium, every player will not change his position provided that the others do not change their positions. „ Therefore, a dominant strategy equilibrium must be a Nash equilibrium. Nash Equilibrium for Prisoner’s Dilemma Game 10,0 2,2 Do not Confess Confess 5,5 0,10 John Do not Confess Confess Peter What is not a Nash equilibrium? „ In the bar scene, Nash suggested everyone should go for his second choice. „ This is not a Nash equilibrium because if you know all the others are going to choose their second choices, then you will certainly change your choice to the most beautiful girl. What is a mixed Nash equilibrium? „ To understand what a mixed Nash equilibrium is, let’s play the following three person game. A three-person game • Each one can show either one finger or two fingers. • If you are the only one showing one finger, then you get one dollar from me. • If you are the only one showing two fingers, then you get two dollars. • Otherwise, everyone gets nothing ! • Can you find the Nash equilibria for this game ? „ Does this game have any dominant strategy equilibrium ? „ How many possible outcomes for this game? How many of them are Nash equilibria? List all of them. Exercise