2. Consider the overlapping generations model that was discussed in e lectures (please see lecture notes for details). Let u(x, y) denote the gent's utility from consuming z when young and y when old. Assume that (2, 1) = 5, u(1, 1) = 4, u(2,0) = 3, u(1,0) = 2. a) Show that there exists a subgame perfect equilibrium where each agent onsumes (1,1) and gets lifetime utility 4 when every agent observes the tire history of past transfers. b) Suppose that each agent t only observes the transfer of the previous gent t - 1. Show that there is a Nash equilibrium which supports the outcome where every agent transfers 1. An equilibrium is sequentially rational if it prescribes optimal choices
2. Consider the overlapping generations model that was discussed in e lectures (please see lecture notes for details). Let u(x, y) denote the gent's utility from consuming z when young and y when old. Assume that (2, 1) = 5, u(1, 1) = 4, u(2,0) = 3, u(1,0) = 2. a) Show that there exists a subgame perfect equilibrium where each agent onsumes (1,1) and gets lifetime utility 4 when every agent observes the tire history of past transfers. b) Suppose that each agent t only observes the transfer of the previous gent t - 1. Show that there is a Nash equilibrium which supports the outcome where every agent transfers 1. An equilibrium is sequentially rational if it prescribes optimal choices
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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![2. Consider the overlapping generations model that was discussed in
the lectures (please see lecture notes for details). Let u(x, y) denote the
agent's utility from consuming a when young and y when old. Assume that
u(2, 1) = 5, u(1, 1) = 4, u(2,0) = 3, u(1,0) = 2.
a) Show that there exists a subgame perfect equilibrium where each agent
consumes (1,1) and gets lifetime utility 4 when every agent observes the
entire history of past transfers.
b) Suppose that each agent t only observes the transfer of the previous
agent t - 1.
Show that there is a Nash equilibrium which supports the outcome
where every agent transfers 1.
. An equilibrium is sequentially rational if it prescribes optimal choices
at every observable history. In this case, there are two observable his-
tories, one where the previous agents transfer was a 1 = 1 and the
second when a 1 = 0. Is there a pure strategy sequentially rational
equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8c433bb-f6f5-4f58-adfd-d3d8e6b44187%2F97ca09b9-caa6-42c9-bd59-29e74fdcf869%2F9yv24r8_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the overlapping generations model that was discussed in
the lectures (please see lecture notes for details). Let u(x, y) denote the
agent's utility from consuming a when young and y when old. Assume that
u(2, 1) = 5, u(1, 1) = 4, u(2,0) = 3, u(1,0) = 2.
a) Show that there exists a subgame perfect equilibrium where each agent
consumes (1,1) and gets lifetime utility 4 when every agent observes the
entire history of past transfers.
b) Suppose that each agent t only observes the transfer of the previous
agent t - 1.
Show that there is a Nash equilibrium which supports the outcome
where every agent transfers 1.
. An equilibrium is sequentially rational if it prescribes optimal choices
at every observable history. In this case, there are two observable his-
tories, one where the previous agents transfer was a 1 = 1 and the
second when a 1 = 0. Is there a pure strategy sequentially rational
equilibrium?
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