# HOMEWORK

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```					                         University of California, Davis -- Department of Economics
ECONOMICS 200C : MICRO THEORY
Professor Giacomo Bonanno
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HOMEWORK 4
Consider the following cases. Assume throughout that the firms are risk-neutral.
CASE 1. Tomorrow, with equal probability, it will either rain or shine. Firms 1 and 2 have to
make their production plans today not knowing what the weather will be like tomorrow.
They simultaneously choose whether to produce umbrellas or sun lotion. Their profits
are as follows: if they make the same choice (both choose umbrellas or both choose
lotion) then they make a profit of 1 each, irrespective of the weather. If they make
different choices, then the firm that makes the choice appropriate to the weather makes
a profit of 4, while the other one makes a profit of 0 (e.g. if firm 1 chooses lotion, firm
2 chooses umbrellas and the weather turns out to be rain, then firm 1 makes a profit of 0
and firm 2 makes a profit of 4).
(a) Draw the extensive-form game.
(b) Write the corresponding normal-form game and find all the pure-strategy Nash equilibria.
CASE 2. Consider now the alternative situation where firm 1 knows with certainty what the
weather will be like (e.g. because it has access to an accurate weather forecast), while
firm 2 does not know (although it is common knowledge that firm 1 knows what the
weather will be like) The production decisions are still made simultaneously (that is, in
ignorance of what the other firm has chosen). [Hint: you can think of this situation as
equivalent to the situation where production decisions are made after the realization of
the weather and firm 1 gets to see what the weather is like, while firm 2 does not.]
(c) Draw the extensive-form of this game.
(d) Write the corresponding normal-form game and find all the pure-strategy Nash equilibria.
CASE 3. Now let's go back to Case 1, where both firms are uncertain about the weather, but
modify it as follows: firm 1 chooses first (not knowing what the weather will be like)
and then firm 2 learns what firm 1 chose and makes its choice second with the
knowledge of what firm 1 did (but not knowing what the weather will be like).
(e) Draw the extensive-form of this game.
(f) Write the corresponding normal-form game and find all the pure-strategy Nash equilibria.
CASE 4: now modify Case 2 (where firm 1 knows the weather before it makes its decision) as
follows: firm 2 knows firm 1's decision but not what the weather is like when it makes
its own decision.
(g) Draw the extensive-form of this game.
(h) Write the corresponding normal-form game and find all the pure-strategy Nash equilibria.
(i) Now compare Case 1 with Case 2: does firm 1 gain from the additional information it
has in Case 2 (the state of the weather) as compared to Case 1? Does firm 2 gain or
suffer from the additional information given to firm 1?
(j) Now compare Case 3 with Case 4: does firm 1 gain from the additional information it
has in Case 4 (the state of the weather) as compared to Case 3? Does firm 2 gain or
suffer from the additional information given to firm 1? Try to explain why this is
the case.

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 views: 17 posted: 6/15/2012 language: English pages: 1