Problem Set #11
- PlSc 349
- Due: Tuesday, 30 November 2010
- [7 points] Problem U9.1
- [6] Problem U9.4
- [8] Problems U9.11
- [3] Problem U9.12
- [18] [modified version from Osborne 2004] A challenger chooses to run
against an incumbent in the next election. The challenger is
strong with probability 1/2 and weak with probability
1/2. The challenger knows her type but the incumbent does not.
The challenger may either ready herself through exploratory polling and fund-raising
for the campaign or remain unready.
(She is already declared, and she cannot
withdraw.) The incumbent observes the challenger's readiness, but not
her type, and chooses whether to campaign or withdraw
from the race.
An unready challenger's payoff is 5 if the incumbent withdraws.
Preparations cost a strong challenger 1 unit of payoff and a weak one
3 units, and an incumbent's campaigning entails a loss of 2 units for
each type. The incumbent prefers to campaign (payoff 1) rather than
to withdraw to (payoff 0) a weak challenger (who is easily defeated),
and prefers to withdraw (payoff 2) rather than to fight (payoff -1)
a strong one. The extensive game below models this situation. The
first move is made by Chance, which determines the challenger's type.
Both types have two actions, Ready and Unready, so that the
Challenger has four strategies. The Incumbent has two information sets,
at each of which it has two actions (Withdraw and Campaign),
and thus also has four strategies. [Payoffs are Challenger (red),
Incumbent (blue).]
- Find all the perfect Bayesian equilibrium/a of this game. [Hint: Try to
simplify the game.]
- Now set the (prior) probability of a Challenger being Strong to 1/8.
Find the perfect Bayesian equilibrium/a of this game.
- Which game is more realistic, considering prior beliefs and
equilibria?
- [4] In the previous problem, what do you expect to happen using
a behavioralist perspective (in both cases)? Refer specifically to
studies from Camerer to support your positions.
- [4] Describe a political situation (not discussed in class or the
reading) that could be characterized as a signalling game. Discuss
whether the outcome is separating, pooling, or partial pooling (semiseparating).
- [for future planning] Which problem was most useful in learning
the concepts? Which problem was least useful?
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