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Economics Problem Set Analysis

The document describes a problem set involving two economic game theory problems. The first problem involves a buyer and seller, where the seller knows the quality of a good but the buyer does not, and the seller has the option to reveal independent test results. The second problem involves a three player game where nature first chooses between 'First' and 'Second'.

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25 views1 page

Economics Problem Set Analysis

The document describes a problem set involving two economic game theory problems. The first problem involves a buyer and seller, where the seller knows the quality of a good but the buyer does not, and the seller has the option to reveal independent test results. The second problem involves a three player game where nature first chooses between 'First' and 'Second'.

Uploaded by

bawar98947
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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BE 510 Business Economics 1 - Autumn 2023

Problem Set 10

1. A seller offers a good to a buyer. The quality of the good is either high or low, and the seller
knows which one it is. The buyer is uncertain; she assumes a (commonly known) prior prob-
ability of high quality of 0.5. If the buyer does not purchase the good, both players earn 0. If
the buyer does buy and the quality is low, her payoff is –2 and the seller’s payoff is 10. If the
buyer acquires a high-quality good, both players earn 5.
Furthermore, the buyer knows that the good on offer has been tested by an independent
agency, but she does not know the result of this test. The seller has the option to reveal the
test result before the buyer decides whether to make the purchase. If he does reveal the result,
the buyer will know the quality (the test is perfectly accurate). Revealing the test result cre-
ates a cost of 1 for the seller such that his possible payoffs of 10, 5, or 0 (see above) would be
reduced to 9, 4, and –1, respectively.
(a) Write down the game in extensive form (i.e., draw the game tree).
(b) Find all pure-strategy Perfect Bayesian Equilibria.
[Hint: The seller can choose from four possible pure strategies. Organize your search for PBEs by consider-
ing each of these cases one after another.]

2. Consider the 3-player game below, in which Nature starts by choosing either ‘First’ or ‘Second’
with probabilities 3/4 and 1/4. Determine a mixed-strategy PBE in which player 2 chooses
‘Up’ for sure, and players 1 and 3 randomize.

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