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 6; if platform m wins, Party L gets 0; if platform / wins, Party L gets -6. Party R's payoffs are as follows. If platform / wins, Party R gets -6; if platform m wins, Party R gets 0; if platform / wins, Party R gets 6. 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 0.9r + 0.17. 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 0 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 6; if platform m wins, Party L gets 0; if platform / wins, Party L gets -6. Party R's payoffs are as follows. If platform / wins, Party R gets -6; if platform m wins, Party R gets 0; if platform / wins, Party R gets 6. 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 0.9r + 0.17. 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 0 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 6; if platform m wins, Party L gets 0; if platform / wins, Party L gets -6.
Party R's payoffs are as follows. If platform / wins, Party R gets -6; if platform m wins, Party R gets 0; if platform / wins, Party R gets 6.
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 0.9r + 0.17. 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 0 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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