Question

Suppose a soccer player has three options when taking a penalty kick: Kick right (KR), kick left (KL), or kick down the center (KC). The goalie can choose to dive right (DR), dive left (DL), or stand in the center (SC). Assume the goalie blocks the kick whenever he guesses correctly (+1) but fails to make the save otherwise (-1). The payoff for the kicker is opposite. The matrix given below shows the payoff each player will get as a result of each strategy. The first number in each box denotes the kicker's payoff, and the second number shows the goalie's payoff. Given this information, fill in the missing values in the given matrix. Goalie (player 2) DL DR SC KR 1,-1 Kicker (player 1) -1, 1 v KL 1,-1 KC 1,-1 In this penalty kick game, there will be

Answer 1

	Goalie: DR	DL	SC
Kicker: KR	-1, 1	1, -1	1, -1
KL	1, -1	-1, 1	1, -1
KC	1, -1	1, -1	-1, 1

(When Kicker KL and Goalie DR, then Kicker will score a goal, so, his payoff will be +1 and Goalie's will be -1. Similarly, we derive all other missing values.)

No Nash equilibrium.
(Their best response can never occur simultaneously, so, there will no NE in pure strategy.)