Information Use the following information to answer questions 1-4. Courtney and Larry are playing one-on-one basketball. This time, they are playing for $100; that is, the loser of the game will pay the winner $100. The game proceeds as follows: one player is on offense, the other is on defense. The player on offense will either score or miss. If the player on offense scores, he or she wins the game. If the player on offense misses, he or she goes to defense, and the other player goes on offense. This process continues until one of them scores. The player on offense always has a 0.2 (1/5) probability of scoring. Question 1 (0.5 points) This is an example of a Question 1 options: Recursive dynamic program. Competitive equilibrium. Non-recursive dynamic program. Simultaneous move game. Mixed strategy equilibrium. Save Question 2 (0.5 points) Not counting win and lose, how many states of play are in this game? Question 2 options: 1 2 3 4 5 Save Question 3 (0.5 points) Suppose that Courtney starts the game on offense. What is the probability that she wins the game? Note that I am not asking the probability that she scores and wins on this possession. Question 3 options: 5/9 2/5 1/2 3/4 4/5 Save Question 4 (0.5 points) If she starts on offense, what is the value of the game for Courtney? Question 4 options: $25 $55.6 ($500/9) $11.1 ($100/9) $50 $0 Save Question 5 (0.5 points) Which of the following could be correctly considered a non-recursive dynamic program/game? Question 5 options: A round of golf, where two golfers play 18 holes, and no hole is repeated. Hockey overtime, where two teams play five minute periods until one of them scores and wins. A tennis match from deuce onwards. A soccer penalty kick, where the kicker decides whether to shoot left or right and the goalie decides to whether dive left or right at the same time. Two basketball players alternate taking full court shots. The first to hit a full court shot is paid $10 by the other. Save Information (Use the following information to answer questions 6-10). Let's play (American) football. Each team, offense or defense, chooses one of its three possible plays, or strategies. Payoffs, in expected yards, are given below. In this case, the offense prefers a higher number of expected yards, while the defense prefers a lower number. The two teams choose their plays at the same time. Defense 4 on the line 5 on the line 6 on the line Pass +5 -5 0 Handoff +5 0 -5 QB Sneak 0 +5 -5 Offense Question 6 (0.5 points) Suppose the defense thinks that the offense will play "Pass." What is(are) the defense's best response(s)? Question 6 options: 4 on the line. 6 on the line. The defense has no best response to this strategy. 5 on the line. 4 on the line or 5 on the line. Save Question 7 (0.5 points) Suppose the offense thinks that the defense will play "4 on the line." What is(are) the offense's best response(s)? Question 7 options: Handoff. Pass or QB sneak. Pass. QB Sneak. Handoff or Pass. Save Question 8 (0.5 points) Is the strategy pair (QB sneak, 6 on the line) a Nash equilibrium? Question 8 options: No; "Handoff" is the best response to "6 on the line." No; "5 on the line" is a best response to "QB Sneak." Yes. No; "4 on the line" is a best response to "QB sneak." No; "Pass" is the best response to "6 on the line." Save Question 9 (0.5 points) Is the strategy pair (Pass, 4 on the line) a Nash equilibrium? Question 9 options: Yes. No; there cannot be a Nash equilibrium in a game with three strategies. No; 5 on the line is the defense's best response to Pass. No; Handoff is the offense's best response to 6 on the line. No; 4 on the line is the defense's best response to Pass. Save Question 10 (0.5 points) Which of the following statements is true? Question 10 options: "Pass" is dominated by "Handoff." "Handoff" is a dominant strategy. "Four on the line" is dominated by "Five on the line." "4 on the line" is dominated by "6 on the line." There is no dominant or dominated strategy in this game. Save Information (Use the following information to answer questions 11-15). Basketball power forward Charles Duncan has two post moves: the jump hook with the left hand and the newly learned drop step. His defender must anticipate one move or the other. The probability that Charles makes the shot is given in the table. (Remember that Charles prefers a high probability, while his defender prefers a low probability!) Defender Anticipate Jump hook Jump hook Anticipate Drop step 0.2 0.6 0.8 0.4 Charles Drop step Question 11 (0.5 points) Which of the following is true about this game? Question 11 options: There is a Nash equilibrium in pure strategies where each player has a dominant strategy. There is a Nash equilibrium in pure strategies where one of the two players has a dominant strategy. Although there is a Nash equilibrium in pure strategies, neither player has a dominant strategy. There is no Nash equilibrium in pure strategies, but there is a Nash equilibrium in mixed strategies. There is neither a Nash equilibrium in pure strategies nor in mixed strategies. Save Question 12 (0.5 points) What is the equilibrium probability that Charles will shoot a jump hook? Question 12 options: 1 0 3/4 1/2 1/4 Save Question 13 (0.5 points) What is the equilibrium probability that the defender plays anticipate a jump hook? Question 13 options: 1 1/4 3/4 0 1/2 Save Question 14 (0.5 points) Now, suppose that the defender plays "anticipate jump hook" at a lower probability than your answer to the previous question. What is Charles's best response? Question 14 options: Always play jump hook. Always play drop step. Match the defender's mixing probabilities. Increase the probability of playing drop step, but still play jump hook with positive probability. Play jump hook with the same probability as your answer to question 12. Save Question 15 (0.5 points) What is the equilibrium probability that Charles will hit the shot? Question 15 options: 1/4 3/5 1/2 9/16 5/16 Save Question 16 (0.5 points) In their study of the mixed strategy hypothesis among professional tennis players, the authors found that professional players Question 16 options: do not mix their strategies properly but do choose strategies randomly. do not mix their strategies properly and do not choose strategies randomly. do mix their strategies properly and do choose strategies randomly. do mix their strategies properly but do not choose randomly. play pure strategies. Save Question 17 (0.5 points) In his study of professional football, \"It's fourth and two\" Romer calculated the Question 17 options: probability of winning given the location. probability of winning given the location, possession, and score. probability of winning given the location and possession. point value of having possession with first and ten for each location. probability of winning given the location, possession, score and time remaining. Save Question 18 (0.5 points) MSU is beating Ohio State 75-56 with 5 minutes left in the game. Suppose that Ohio State makes 60% of its two point shots, but only 40% of its three point shots. Thus, if Ohio State shoots only three pointers instead of shooting two pointers, it will score the same expected number of points, but the variance of its scoring will be greater. Ohio State's coach tells his team to shoot only three point shots from now on. What is the coach doing? Question 18 options: Switching from a pure strategy to a mixed strategy. Playing a strategic move by injecting uncertainty into the game. Throwing the game away by having his team take shots that are less likely to go in. Playing a dominated strategy. Choosing a strategy randomly, since three points shots yield as many points, on average, as two point shots. Save Information (Use the following information to answer questions 19-20). Now let's play baseball, this time with only three strategies. Probability of the Batter getting on base, given any two strategies, is given in the table below. Remember that the Fielder prefers a lower probability, while the Batter prefers a higher probability. Fielder Bunt Infield Right field Left field 0.300 0.300 0.350 0.350 0.250 0.100 0.100 0.200 0.150 Batter Swing Hard Opposite Field Question 19 (0.5 points) How many pure strategy Nash Equilibria are there in this game? Question 19 options: None. 1 2 3 4 Save Question 20 (0.5 points) Which of the following is true about this game? Question 20 options: The Batter has a dominant strategy. The Fielder has a dominant strategy. Neither team has a dominant strategy, but the Fielder has a dominated strategy. Neither team has a dominant strategy, and neither team has a dominated strategy. Neither team has a dominant strategy, but the Batter has a dominated strategy. Save Question 21 (0.25 points) BONUS: According to the lecture, which NFL coach contacted David Romer to discuss his paper, "It's Fourth and Two?" Question 21 options: Jim Harbaugh. Vince Lombardi. Jim Caldwell. Bill Belichick. Pete Carroll. Save Save All Responses