Question

Cart and Robert are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Carl would prefer to see one movie (call it movie C) and Robert would prefer to see the other movie (movie R), but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Robert'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. Robert Moviec 164 Moviec Movie R 0.0 Suppose Robert 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 Carl, he uses a smartphone app to observe Carl's location using GPS. Because Robert can see whether Cart heads in the direction of movie C or movie Rhe can base his decision on Carl's decision Carr phone alerts him that Robert is tracking Nm. Carl still has the same strategies available, but Robert 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 Robert chooses, followed by a vertical bar, followed by the letter for the corresponding movie Carichose. If Robert decides to choose movie conditional on Cart's choosing movie and conditional on Cart's choosing movie R (that is, he chooses to always go to movie C), he is playing strategy 3 strategy 4 strategy 1 the strategies that Robert chooses and the actions Carl chooses. Complete the following table by choosing the correct payoffs accord Carl's payoff is given first, as in the preceding payoff matrix. strategy 2

Answer 1

He is playing strategy 2

Table :

	Strategy 1	strategy 2	strategy 3	strategy 4
	R|C : R|R	C|C : C|R	C|C: R|R	R|C: C|R
Movie C	(0,0)	(16,4)	(16,4)	(0,0)
Movie R	(4,16)	(0,0)	(4,16)	(0,0)

Solution of sequential game

option 2), 3) 5)

• Carl choose movie C & Robert plays strategy 2

• Carl goes for R , Robert plays 1

• Carl goes for C, Robert plays 3

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