What should be the new A Beautiful Mind solution concept Suppose we have a theory which can predict the outcome (solution)of a game.What property should this solution has? -Suppose we have a theory which predicts that player 1,2,3 must choose A,B,C respectively,i.e.(A,B,C)is the solution of the game. What should be the new Nash Equilibrium solution concept Now if player 1 knows that player 2 and player 3 are going to choose B and The decisions of the players is a Nash C respectively,will he change his choice Equilibrium if no individual will change A? his position,given that the others do not .No,if the theory works.Similarly player change their positions. 2 and player 3 will not change their choices if the others don't. An Example of a Nash Equilibrium Splitting the bill .10 classmates are having In a very boring lecture,all of the students dinner together.Each one would like to leave the classroom early,but has the choice of a cheaper meal for 50 dollars or an no one is willing to leave before the end of excellent meal for 80 dollars. the lecture unless someone else leaves first. As usual,they decide to split the bill. Therefore,every student will choose to stay until the end of the lecture and this is a Everyone chooses the cheaper meal is not a Nash Nash Equilibrium. equilibrium. How about everyone chooses the excellent meal? 99 A Beautiful Mind What should be the new solution concept ? „ Suppose we have a theory which can predict the outcome (solution) of a game. What property should this solution has? „ Suppose we have a theory which predicts that player 1,2,3 must choose A, B, C respectively, i.e. (A,B,C) is the solution of the game. What should be the new solution concept ? „ Now if player 1 knows that player 2 and player 3 are going to choose B and C respectively, will he change his choice A? „ No, if the theory works. Similarly player 2 and player 3 will not change their choices if the others don’t. Nash Equilibrium „ The decisions of the players is a Nash Equilibrium if no individual will change his position, given that the others do not change their positions. An Example of a Nash Equilibrium „ In a very boring lecture, all of the students would like to leave the classroom early, but no one is willing to leave before the end of the lecture unless someone else leaves first. „ Therefore, every student will choose to stay until the end of the lecture and this is a Nash Equilibrium. Splitting the bill „ 10 classmates are having dinner together. Each one has the choice of a cheaper meal for 50 dollars or an excellent meal for 80 dollars. As usual, they decide to split the bill. „ Everyone chooses the cheaper meal is not a Nash equilibrium. „ How about everyone chooses the excellent meal?