Question

1. Consider the following game between a penalty kicker and a goalkeeper: Goalie Left Center Right 30,70 60,40 80,20 40,60 20,80 40,60 70,30 60,40 40,60 Left Center Right Kicker (a) Show that the kicker has a mixed strategy that strictly dominates the 'center' strategy. (b) Show that having eliminated the kicker's 'center' strategy, the goalie will not want to play 'center'.

Answer 1

Solution: 1 Giren game between penalty kickey and a goalkeeper. Goalie left conter 30,70 60140 40,60 90, 80 Kickey Right 80,20 4960 be Center le Right 70, 30 60,40 40,60 @ kicker has a mixed strategy that strictly dominates the "Center' strategy - Taking up kicker first: the strategy of center has been weakly dominated by the strategy Right. In other words: (7o, 6o, yo) = (40,20,40) from matrix Thus, strategy Right is eliminated Goalie: similarly center strategy is dominating strategy Right. Thus, right strategy is eliminated.

b If Kicker's Comter Strategy eliminated, the goalie will not want to play Center? -) If kicker center strategy is eliminated, now kicker will go with strategy left. It will not be profitable for goalie to adopt center strategy it Kicker goes with left strategy (70740) _ o_