Game Theory: Messi has been awarded a penalty kick. U.S.A.’s goalie, Howard, has

Question

Game Theory: Messi has been awarded a penalty kick. U.S.A.’s goalie, Howard, has two possible strategies, to dive to his left or dive to his right. Messi can shoot to both sides. There is no time for the goalie to determine where the ball is going before he must commit himself to diving left or right. Suppose that the Howard stops the shot with a 50 percent chance if Messi shoots right and the goalie dives left. When he kicks left the goalie stops the shot 25 percent of the time if he dives right. On the other hand, Messi always scores if he shoots right or left uncontested. Summarize this game in a matrix with the expected payoffs (if Messi scores, his payoff is 1 and Howard is 0, and if Messi doesn’t score his payoff is 0 and Howard’s payoff is 1)

Explanation / Answer

Left = L, Right = R

1). (L,L) and (R,R) will lead to a goal which will be uncontested. so Messi will get 1 and howard will get 0 in both .

2). (L,R) =(0.75,0.25) because there is 25% chance that goal will be stopped by Howard. He will get 1 if he stops the goal. With 25% chance, his expected payoff will be 0.25. Similarly , for Messi there is 75% chance of goal and with payoff of 1 , his expected payoff will be 0.75.

3). (R,L) = (0.5,0.5) with the same logic as in part 2.

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.