Two staff managers in the ΠBΦ sorority, the house manager (player 1) and kitchen manager (player 2), must select a resident assistant from a poolof three candidates: {a, b, c}. Player 1 prefers a to b, and b to c. Player 2 prefers b to a, and a toc. The process that is imposed on them is as follows: First, the house manager vetoes one of thecandidates and announces the veto to the central office for staff selection and to the kitchenmanager. Next the kitchen manager vetoes one of the remaining two candidates and announcesit to the central office. Finally the director of the central office assigns the remaining candidateto be a resident assistant at ΠBΦ.a. Model this as an extensive-form game (using a game tree). You will need to define theutilities of both players.b. Find the subgame-perfect Nash equilibrium (or equilibria) for this game. Is it unique?c. Now assume that before the two players play the game, player 2 can send an alienatinge-mail to one of the candidates, which would result in that candidate withdrawing herapplication. Would player 2 choose to do this, and if so, with which candidate?
Two staff managers in the ΠBΦ sorority, the house manager (player 1) and kitchen manager (player 2), must select a resident assistant from a pool
of three candidates: {a, b, c}. Player 1 prefers a to b, and b to c. Player 2 prefers b to a, and a to
c. The process that is imposed on them is as follows: First, the house manager vetoes one of the
candidates and announces the veto to the central office for staff selection and to the kitchen
manager. Next the kitchen manager vetoes one of the remaining two candidates and announces
it to the central office. Finally the director of the central office assigns the remaining candidate
to be a resident assistant at ΠBΦ.
a. Model this as an extensive-form game (using a game tree). You will need to define the
utilities of both players.
b. Find the subgame-perfect Nash equilibrium (or equilibria) for this game. Is it unique?
c. Now assume that before the two players play the game, player 2 can send an alienating
e-mail to one of the candidates, which would result in that candidate withdrawing her
application. Would player 2 choose to do this, and if so, with which candidate?
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