Consider an extensive game. First, a firm from 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 o§er is accepted, the payffs to Betty and the firm are (y1 - x1; 1- y1), where x1 is the house price in City 1. While Betty is contemplating over this o§er, 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 2ís offer and accepts the outside option, the payoffs to the two players are (y2 - x2; 0). If Betty rejects both offers, then the payo§s are (0; 0). Assume y1 > x1, y2 > x2, 0 < y1 < 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: (a) Draw the game tree. (b) Find the subgame perfect equilibrium (SPE) by specifying strategies used. (c) What is Bettyís payoff in the SPE? How does this payoff change respectively with x1, y2, and x2?
Consider an extensive game. First, a firm from 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 o§er is accepted, the payffs
to Betty and the firm are (y1 - x1; 1- y1), where x1 is the house price in
City 1. While Betty is contemplating over this o§er, 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 2ís offer and accepts the outside
option, the payoffs to the two players are (y2 - x2; 0). If Betty rejects both
offers, then the payo§s are (0; 0). Assume y1 > x1, y2 > x2, 0 < y1 < 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: (a) Draw the
game tree. (b) Find the subgame perfect equilibrium (SPE) by specifying
strategies used. (c) What is Bettyís payoff in the SPE? How does this payoff
change respectively with x1, y2, and x2?
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