Consider the following game between a penalty kicker and a goalkeeper:
goalie kicker left center right left center right 30; 70 60; 40 80; 20 40; 60 20; 80 40; 60 70; 30 60; 40 40; 60

(a) show that the kicker has a mixed strategy that strictly dominates the ícenterístrategy.
(b) show that having eliminated the kickerís ícenterístrategy, the goalie will not want to play ëcenterí.
(c) now consider the 2x2 game goalie kicker left right left right 30; 70 80; 20 70; 30 40; 60 find all nash equilibria.
(d) derive the expected payo§s to the two players at the equilibrium/equilibria.
(e) explain why the players may want to play mixed strategies in this game.
(f) the assurance game also has a mixed strategy equilibrium.

does the reasoning from part (e) apply in this case? explain your answer.