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5. Finding Nash equilibria in sequential games Hubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to see one movie (call it movie H) and Larry would prefer to see the other movie (movie L). but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power cutting the conversation short. Both movies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The following payoff matrix represents the game they are playing. Larry Movie H Movie L Movie H 14. 6 0. 0 Hubert Movies L 6. 14 Suppose Larry is near home and quickly starts charging his phone. At home, however he gets terrible phone service but a strong wireless signal. Therefore, instead of calling Hubert, he uses a smartphone app to observe Hubert's location using GPS. Because Larry can see whether Hubert heads in the direction of movie H or movie L. he can base his decision on Hubert's decision. Hubert's phone alerts him that Larry is tracking him. Hubert still has the same strategies available, but Larry now has four possible strategies. The following table represents the sequential version of this game in normal form. The table shows each strategy as the letter for the movie Larry chooses, followed by a vertical bar, followed by the letter for the corresponding movie Hubert chose. Larry Strategy 1 Strategy 2 Strategy 3 Strategy 4 HIH; LIL HIH: HIL LIH; LIL LIH; HIL Hubert Movie H Movie L If Larry decides to choose movie L conditional on Hubert's choosing movie H and L conditional on Hubert's choosing movie L (that is, he chooses to always go to movie L), he is playing Complete the previous table by choosing the correct payoffs according to each of the strategies that Larry chooses and the actions Hubert chooses. Hubert's payoff is given first, as in the preceding payoff matrix. Which of the following represent a Nash equilibrium in this sequential version of the game? Check all chat apply. Hubert goes to movie L and Larry plays strategy 2 Hubert goes to movie H and Larry plays strategy 3 Hubert goes to movie L and Larry plays strategy 3 O Hubert goes to movie H and Larry plays strategy 2 O) Hubert goes to movie H and Larry plays strategy 1If Larry decides to choose movie L conditional on Hubert's choosing movie always go to movie L), he is playing strategy 1 Complete the previous table by choo ect payoffs according to e Hubert's payoff is given first, as in th strategy 4 payoff matrix. strategy 3 Which of the following represent a N m in this sequential versi strategy 2Strategy 1 Strategy 2 HIH; LIL HIH; HIL Hubert Movie H Movie L 0. 0 If Larry decides to che 0. 0 vie L conditional always go to movie L 14, 0 laying 14, 6 Complete the previous y choosing the c Hubert's payoff is give 8, 14 95 in the precediLarr Strategy 1 Strategy 2 HIH: LIL HIH; HIL Movie H Movie L 0. 6 decides to chi Ivie L conditional on o to movie LI 14. 8 laying 14. 0 the previou 0.0 by choosing the corr payoff is give as in the preceding 6, 14 the following represent a Nash equilibrioLarry 7 1 Strategy 2 Strategy 3 Stra IL HIH: HIL LIH: LIL LIF vie L c 14, 6 al on Hubert's choosing laying 14. 0 by cho correct payoffs accord as in t 0. 0 eding payoff matrix.Larry Strategy 1 Strategy 2 Strategy 3 Strategy IH; LIL HIH; HIL LIH LIL LIH: H 0. 14 se movie L el on Hubert's choosing mov he is playing 14, 0 0. 0 able by cho 0. 8 2 correct payont's according to first, as in ding payoff matrix. 14, 6 epresent a Nash equilibrium in this sequential veLarry Strategy 3 Strategy LIH; LIL LIH; HIL 14 I on choosing movie H corre It's according to ead ding atrix. librium in HersionLarry ategy 2 Strategy 3 Strategy 4 H: HIL LIH: LIL LIH; HIL 14. 0 itional on choosing movie H and L co 6. 14 0.0 the corre 14, 6 If's according to each of the receding atrix. 0. 0 equilibrium in this sequential version of theStrategy 4 LIN: HIL 009 ie H and L cond 300 beach of the strely 3 Strategy IL LIH; HIL 0. 0 : choos hie H and L condition 14, 0 OfIs aCO 14 o each of the strateg is sequential version of the game
