For the next three questions, consider the game shown below. L R T 30,30 50,35 B 40,60 20,20 What is/are the Nash Equilibrium/Equilibria if choices are made simultaneously? The Nash Equilibrium/Equilibria is/are Select one: O a. (T, L) and (B, R) O b. (B, L) O C. (T, R) O d. (B, R) O e. (T, L) Of. (T, R) and (B, L) What is the SPE outcome if player 1 chooses first? The SPE outcome is Select one: O a. (T, R) and (B, L) O b. (T, R) O c. (B, L) What is the SPE outcome if player 2 chooses first? The SPE outcome is Select one: O a. (T, R) and (B, L) O b. (B, L) O C. (T, R)For the next two questions, suppose three pirates of different ages have a treasure of 100 gold coins. They decide to split the coins using this scheme: - The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it. u If more than 50% (exclusive) of the pirates vote for it, then the coins will be shared that way and the game ends. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. Note that if exactly 50% of the pirates vote for it, then the pirate proposing the scheme will be thrown overboard. a As pirates tend to be a bloodthirsty bunch. If a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. . Assuming that all 3 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates). what will happen? ' I Wm . H B Path: p Assume now Captain Hook spots the scene and wants to share the gold as well. That is, now we have four pirates sharing the coins. Captain Hook will be the rst to propose a scheme to share the coins. Assume the same rule applies. What will happen? For the next two questions. consider two firms with the same constant average and marginal cost, Week 9 lecture recording AU - IVIU - U [Incanmy me cost function is TC1 = 5q1, TC2 = 5q2), facing the market demand curve q1 + q2 = 53- P. We will use the Stackelberg model to analyze what will happen if one of thes firm makes its output decision before the other. What is each firm's equilibrium output and prot if they behave noncooperatively and move simultaneously? The equilibrium output and profit are Select one: O a. q1 = 18; m1 = 216; q2 = 18; 12 = 216 O b. q1 = 16; m1 = 256; q2 = 16; 12 = 256 O c. q1 = 12; my = 288; 92 = 12; n2 = 288 O d. q1 = 14; my = 280; q2 = 14; 12 = 280 Now suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). What is each firm's equilibrium output and profit? The equilibrium output and profit are Select one: O a. q1 = 26; m1 = 312; q2 = 10; 12 = 120 O b. q1 = 24; m1 = 288; 92 = 12; 12 = 144 O c. q1 = 16; my = 256; q2 = 16; 12 = 256 O d. q1 = 22; m1 = 264; 92 = 14; 12 = 168For the next two questions, use the game shown below U D 2 2 A B Y Z W W AND E G H L/ aww- - ON NYY WON VU - Find the SPE outcome. The SPE outcome is Select one: O a. (U, A) O b. (D, Z, M) O c. (U, B, F) O d. (D, Y, H) Give the complete SPE strategy. The SPE is Select one: O a. (DM, Z, H) O b. (UM, BZ, FH) O C. (DM, BZ, FH) O d. (D, Z, M)For the next two questions, see the game shown below: 1 Find the SPE outcome. The SPE outcome is Select one: 0 a. (D.R,Y) O b. (U, L) O c. (D. R,Z) 0 d. (D. L) Could player 2 improve her payoff by committing to a certain strategy in advance? If so, what strategy should she commit to and what are the new payoffs? Select one: 0 a. Yes. Player 2 should commit to picking L in any circumstance. O b. Yes. Player 2 should commit to picking R in any circumstance. O c. No. Player 2 cannot improve her payoff