Question

For the following question, consider only x > 0: CM R 3,1 - - - - - - - А/ x, \в { 0, x А/ 0,x \в 1,0 1. (5 points) Write this game in normal form. 2. (10 points) Consider the game we would have if we took out the strategy R. For each value of x find all the equilibria of this game. 3. (10 points) For what values of x is playing R the only rationalizable strat- egy for Player 1? 4. (10 points) For what values of x do we have that the game has only pure strategy Nash equilibria?

Answer 1

pa x, 1 ox TO M P1 L la, I Since xso given. so, let starting with x=1 PA . L M 1, 1 o, l o, 1 1, o Pure strategy equila i P.1 plays , P2 is indifferent bt Aff pa plays M , pa will choose A if P2 plays ,P1 will play L P2 plays B , P. 1 will play B. so equilibrium will be LA (11) DBE Things to do

Now x =2 Similarly using the above strategy you best response of both players cases is underlined So, there is no pure strategy nash equel 3. For all values of a hero then greater than o R is the only rationalizable. strategy for P1 ( xol Fray na ned P1 could have mox Playing the game tree. payoff of 1 playing L ar M. 14x²2 yen will plays M he get payoff 6 mA oco,2) because PD in that case will definately choose A of P1 plays L P Q will play B and pa will get payoff of o

so for any 2 x>0, R will give P1 Uо рок з 40 For x = we get only pure strategy nash equilibrium if we look out the strategy Rob Things to do