Question 3. The following game is called centipede game. Two players (Yellow and

Question

Question 3. The following game is called centipede game. Two players (Yellow and Black) choose between “Continue" and “Stop" alternatively. (Yellow goes first, followed by Black, then by Yellow so on and so forth). In the payoff vector, the first element indicates the payoff to Yellow, the second to Black. Suppose both players are rational and only care about themselves. Which of the following is the roll-back equilibrium outcome? Continue Continue Continue Continue Continue Continue 64 Stop Stop Stop Stop 8 32 16 128 b) (8, 32) c) (32, 128) d) (256, 64) Question 4. Along a stretch of beach are 600 children in four clusters, labeled as A, B, C, D. 100 children are located at A, 200 at B, 100 at C, and 200 at D. Two ice-cream vendors are deciding simultaneously where to locate. They must choose the exact location of one of the clusters If there is a vendor in a cluster, all the children in that cluster will buy an ice cream. For clusters without a vendor, half of the children are willing to walk to a vendor who is one cluster away. Nobody is willing to walk the distance of two or more clusters. The ice cream melts quickly; so the walkers cannot buy for the non-walkers. If the two vendors choose the same cluster, each will get a 50% share of the total demand for ice cream. If they choose different clusters, then those children (locals or walkers) for whom one vendor is closer than the other will go to the closer one, and those for whom the two are equidistant will split 50% each. Each vendor seeks to maximize her own sales. Which of the following correctly describes the Nash equilibrium location of the two vendors? a) (B,B) and (D,D) b) (B,C) and (C,B) c) (B,D) and (D,B) d) (A,D) and (D,A) 2 12002 250 240 232s 10 0 20

Explanation / Answer

3. A

4. C

5. D

6. D

7. A

8. C

9. C

10. A

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