Consider an extensive game. First, a firm in City 1 (Player 2) makes Betty (Player 1) a job offer. The offer promises an income y₁. Then Betty decides whether to accept the offer. If the offer is accepted, the payoffs to Betty and the firm are (y1x1, 11), where x₁ is the house price in City 1. While Betty is contemplating over this offer, she receives another job offer from a firm in City 2. This outside option promises an income of y2 and a house price x2. If Betty rejects Player 2's offer and accepts the outside option, the payoffs to the two players are (y2- If Betty rejects both offers, then the payoffs are (0,0). Assume y1 > x1, Y2 > x2, 0 < 1 < 1 and Y2 − x2 + x1 ≤ 1. Assume that Betty will accept an offer if she is indifferent from accepting and rejecting it. Do the following: - x2,0).
Consider an extensive game. First, a firm in City 1 (Player 2) makes Betty (Player 1) a job offer. The offer promises an income y₁. Then Betty decides whether to accept the offer. If the offer is accepted, the payoffs to Betty and the firm are (y1x1, 11), where x₁ is the house price in City 1. While Betty is contemplating over this offer, she receives another job offer from a firm in City 2. This outside option promises an income of y2 and a house price x2. If Betty rejects Player 2's offer and accepts the outside option, the payoffs to the two players are (y2- If Betty rejects both offers, then the payoffs are (0,0). Assume y1 > x1, Y2 > x2, 0 < 1 < 1 and Y2 − x2 + x1 ≤ 1. Assume that Betty will accept an offer if she is indifferent from accepting and rejecting it. Do the following: - x2,0).
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
Related questions
Question
Please see the attachment and asnwer questions.
(a) Draw the game tree. Make sure to specify on the tree the decision makers, actions, and final payoffs.
(b) Find the subgame perfect equilibrium (SPE) by specifying optimal strategies used.
(c) What is Betty's payoff in the SPE? How does this payoff change respectively with x1, y2, and x2? What is the intuition for these results?
Transcribed Image Text:Consider an extensive game. First, a firm in City 1 (Player 2) makes Betty (Player
1) a job offer. The offer promises an income y₁. Then Betty decides whether to
accept the offer. If the offer is accepted, the payoffs to Betty and the firm are
(y1x1, 11), where x₁ is the house price in City 1. While Betty is contemplating
over this offer, she receives another job offer from a firm in City 2. This outside
option promises an income of y2 and a house price x2. If Betty rejects Player 2's
offer and accepts the outside option, the payoffs to the two players are (y2-
If Betty rejects both offers, then the payoffs are (0,0). Assume y1 > x1, Y2 > x2,
0 < 1 < 1 and Y2 − x2 + x1 ≤ 1. Assume that Betty will accept an offer if she is
indifferent from accepting and rejecting it. Do the following:
- x2,0).
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