Answer to Question #254200 in Microeconomics for Leah

Question

Consider the following two-person simultaneous move game: column

left right up 7,3 a,a down a,a 7,3

row

Determine the Nash equilibrium/equilibria for any value of a.

b) Suppose 𝑎 = 4 will there be a Nash equilibrium in a sequential game? Assuming Column is the leader in this game show whether or not there is a Nash-equilibrium in this game

Answer 1

(a)

In this game, there is no dominant strategy. Suppose the 2nd player is playing opera, then the best thing for the 1st player to do is to play opera, too.

Hence, opera is the best response for the 1st player against opera. Similarly, opera is the best response for the 2nd player against opera. Thus, at (opera, opera) neither party wants to take a different action. This is the Nash Equilibrium for the game.

(b)

Given a=4, there will be a nash equilibrium in a sequential game. This is because there will still be no dominant strategy and the nash equilibrium won't change.

If column is the leader, there won't be a nash equilibrium.