Consider the following game, where X = 0: Firm.2 H L Firm.1 H 140,140 20,160 L 9

Question

Consider the following game, where X = 0:
Firm.2
H L
Firm.1 H 140,140 20,160
L 90+x,90-x 50,50

a) For what values of X do both ?rms have a dominant strategy? What is
the Nash equilibrium (or equilibria) in this case?
b) For what values of X only one ?rm has a dominant strategy? What is the
Nash equilibrium (or equilibria) in this case?
c) Are there any values of ? such that neither ?rm has a dominant strategy?
Ignoring mixed strategies, is the a Nash equilibrium in this case?
d) Set X = 0 and compute the mixed strategy Nash Equilibrium in this
game.
e) For any value of X for which there is no "normal" Nash Equilibrium (see
c)) compute the mixed strategy Nash equilibrium.

Explanation / Answer

a) All values x>50 ; Nash Equilibrium: 50, 50 b) All values 40

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