Two political parties, Party L and Party R, are choosing their platforms before an election. The platforms available to each party are 1, m and r. If both parties pick the same platform, that platform wins. If parties pick different platforms, then platform m wins by default. Party L's payoffs are as follows. If platform / wins, Party L gets 8; if platform m wins, Party L gets 0; if platform r wins, Party L gets -8. Party R's payoffs are as follows. If platform / wins, Party R gets -8; if platform m wins, Party R gets 0; if platform r wins, Party R gets 8. How many pure strategy Nash equilibria does this game have? How many inadmissible pure strategy Nash equilibria does this game have? Suppose Party R plays 0.3r +0.7m. What is Party L's expected payoff when it plays its best response to this strategy? Suppose Party L plays 0.2r+ 0.81. What is Party R's expected payoff when it plays its best response to this strategy? Select all correct statements. a. There exists a mixed strategy Nash equilibrium in which Party R plays / with positive probability. ☐ b. There exists a mixed strategy Nash equilibrium in which Party R plays r with O probability, and Party L plays more than one of its strategies with positive probability. ☐ C. There exists a mixed strategy Nash equilibrium in which Party R plays m with positive probability.
Two political parties, Party L and Party R, are choosing their platforms before an election. The platforms available to each party are 1, m and r. If both parties pick the same platform, that platform wins. If parties pick different platforms, then platform m wins by default. Party L's payoffs are as follows. If platform / wins, Party L gets 8; if platform m wins, Party L gets 0; if platform r wins, Party L gets -8. Party R's payoffs are as follows. If platform / wins, Party R gets -8; if platform m wins, Party R gets 0; if platform r wins, Party R gets 8. How many pure strategy Nash equilibria does this game have? How many inadmissible pure strategy Nash equilibria does this game have? Suppose Party R plays 0.3r +0.7m. What is Party L's expected payoff when it plays its best response to this strategy? Suppose Party L plays 0.2r+ 0.81. What is Party R's expected payoff when it plays its best response to this strategy? Select all correct statements. a. There exists a mixed strategy Nash equilibrium in which Party R plays / with positive probability. ☐ b. There exists a mixed strategy Nash equilibrium in which Party R plays r with O probability, and Party L plays more than one of its strategies with positive probability. ☐ C. There exists a mixed strategy Nash equilibrium in which Party R plays m with positive probability.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Two political parties, Party L and Party R, are choosing their platforms before an
election. The platforms available to each party are 1, m and r. If both parties pick
the same platform, that platform wins. If parties pick different platforms, then
platform m wins by default.
Party L's payoffs are as follows. If platform / wins, Party L gets 8; if platform m
wins, Party L gets 0; if platform r wins, Party L gets -8.
Party R's payoffs are as follows. If platform / wins, Party R gets -8; if platform m
wins, Party R gets 0; if platform r wins, Party R gets 8.
How many pure strategy Nash equilibria does this game have?
How many inadmissible pure strategy Nash equilibria does this game have?
Suppose Party R plays 0.3r +0.7m. What is Party L's expected payoff when it
plays its best response to this strategy?
Suppose Party L plays 0.2r+ 0.81. What is Party R's expected payoff when it plays
its best response to this strategy?
Select all correct statements.
a.
There exists a mixed strategy Nash equilibrium in which Party R plays / with
positive probability.
☐ b. There exists a mixed strategy Nash equilibrium in which Party R plays r with
O probability, and Party L plays more than one of its strategies with positive
probability.
☐ C. There exists a mixed strategy Nash equilibrium in which Party R plays m
with positive probability.
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