Game theory question Games Strategies and Decision Making Se

Game theory question:

Games, Strategies, and Decision Making, Second Edition

chapter 2 problem 14:

There are four shoppers in a store--A, B, C and D--who sequentially show up at two checkout lines: line number 1 and line number 2. Initially, both checkout lines are empty. A shows up first, sees which line Amy entered, and chooses between the two lines. B shows up next, sees no one in either line, and chooses one of the two lines. Next, C shows up. She sees A and B in line and chooses between the two lines. Finally, D arrives, sees A, B, and C waiting in line, and enters one of the two lines. Assume a player\'s payoff equals 5 minus the number of shoppers in line ahead of him or her.

a. Derive the extensive form game

b. Now suppose that by the time that D shows up, A has already checked out. Thus, only B and C are in line. Derive the extensive form game.

Solution

a. A enters either line A or line B

B enters the line not chosen by A

c chooses either line 1 or line 2

D choose line one person ahead and not two person ahead.

b. If by the time that D shows up, A has already checked out then he will choose either line with B or with C.