Kate (K) and Meghan (M) simultaneously choose contributions k € [0, 1] and m € [0, 1], respectively. That is, each of them chooses a contribution which is a real number between zero and one (included). Their payoffs are given by um(k, m) = 2k — m and uk (k, m) = 2m - k, respectively. - (a) Find the set of strategies that survive the iterated elimination of dominated strategies, and find all the Nash equilibria of the game. (b) Assume now that Megan and Kate play an infinitely repeated game where the stage game is the contribution game just presented. The discount factor is equal to 8. Find the values of d for which the fully cooperative outcome (m = k = 1) is feasible in equilibrium.
Kate (K) and Meghan (M) simultaneously choose contributions k € [0, 1] and m € [0, 1], respectively. That is, each of them chooses a contribution which is a real number between zero and one (included). Their payoffs are given by um(k, m) = 2k — m and uk (k, m) = 2m - k, respectively. - (a) Find the set of strategies that survive the iterated elimination of dominated strategies, and find all the Nash equilibria of the game. (b) Assume now that Megan and Kate play an infinitely repeated game where the stage game is the contribution game just presented. The discount factor is equal to 8. Find the values of d for which the fully cooperative outcome (m = k = 1) is feasible in equilibrium.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![i tys
Kate (K) and Meghan (M) simultaneously choose contributions k € [0, 1] and m € [0, 1], respectively.
That is, each of them chooses a contribution which is a real number between zero and one (included).
Their payoffs are given by um(k, m) = 2k — m and uk (k, m) = 2m – k, respectively.
-
(a) Find the set of strategies that survive the iterated elimination of dominated strategies, and
find all the Nash equilibria of the game.
(b) Assume now that Megan and Kate play an infinitely repeated game where the stage game is
the contribution game just presented. The discount factor is equal to 8. Find the values of d
for which the fully cooperative outcome (m = k = 1) is feasible in equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84969f1e-da5a-469a-b31e-a98db3267256%2Fae751fd4-0406-4cdf-96dc-55096e727df8%2Fku1vy3_processed.png&w=3840&q=75)
Transcribed Image Text:i tys
Kate (K) and Meghan (M) simultaneously choose contributions k € [0, 1] and m € [0, 1], respectively.
That is, each of them chooses a contribution which is a real number between zero and one (included).
Their payoffs are given by um(k, m) = 2k — m and uk (k, m) = 2m – k, respectively.
-
(a) Find the set of strategies that survive the iterated elimination of dominated strategies, and
find all the Nash equilibria of the game.
(b) Assume now that Megan and Kate play an infinitely repeated game where the stage game is
the contribution game just presented. The discount factor is equal to 8. Find the values of d
for which the fully cooperative outcome (m = k = 1) is feasible in equilibrium.
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