Problem Set 3

Question 1

a. In the game Rock-Paper-Scissors, who are the players,  what are the strategies and what are the payoffs?

b. Write down the game in normal form.

c. Is {Rock, Rock} a Nash equilibrium? Why or why not?

Question 2

Consider the penalty kick game above.

a. What is the Nash equilibrium of the game?  Provide an intuitive explanation for the result.

b. Change the payoff in the lower right corner from (-1, 1) to (-2, 2). What is the Nash equilibrium of the new game? Explain any difference in prediction between the original game and the new game.

Question 3

Watch these two videos and then write down a game in normal form to describe the penalty kick situation. 

Question 4

Download the data of English Premier League penalty kicks from here.

a. Using your game described in (3) find the probability of each case in the data and represent it in a table.

b. Is the observed behavior in the data consistent with the prediction of the model?

c. Using a GMM estimator determine how the payoffs of the game in (3) change based on the footedness of the kicker.