Q3. Bayesian Games An insurer sells insurance to a buyer who has private information about his own expected loss. Without insurance, the buyer's payoff is -1.20, and it is common knowledge that {2,4,6}, each type occurring with equal (1/3) probability. The insurer is better able to take the loss and only suffers -0; for simplicity, the insurer is only able to offer a premium (flat price of insurance) p, which the buyer can accept or reject. The insurer's rejection payoff is 0. If the offer is accepted, the insurer's payoff is p-0, and the buyer's payoff is -p. [I'll do the first part for you: Unconditional on anything, E[0] = 3 * 2 + 3 * 4 + 3 * 6 = 4.] a. Prior to actually solving, explain in words what a "lemons problem" is and why this qualifies. b. For part (b) only, suppose that the insurer observes 0. Solve for the unique SPNE in this game of perfect information; the answer will be in terms of 0. c. Now solve for the (sequentially rational) BNE given the insurer doesn't observe 0. d. Explain (in words) how a penalty (or a tax, if you're Justice Roberts) for refusing to buy insurance could solve the lemons problem.
Q3. Bayesian Games An insurer sells insurance to a buyer who has private information about his own expected loss. Without insurance, the buyer's payoff is -1.20, and it is common knowledge that {2,4,6}, each type occurring with equal (1/3) probability. The insurer is better able to take the loss and only suffers -0; for simplicity, the insurer is only able to offer a premium (flat price of insurance) p, which the buyer can accept or reject. The insurer's rejection payoff is 0. If the offer is accepted, the insurer's payoff is p-0, and the buyer's payoff is -p. [I'll do the first part for you: Unconditional on anything, E[0] = 3 * 2 + 3 * 4 + 3 * 6 = 4.] a. Prior to actually solving, explain in words what a "lemons problem" is and why this qualifies. b. For part (b) only, suppose that the insurer observes 0. Solve for the unique SPNE in this game of perfect information; the answer will be in terms of 0. c. Now solve for the (sequentially rational) BNE given the insurer doesn't observe 0. d. Explain (in words) how a penalty (or a tax, if you're Justice Roberts) for refusing to buy insurance could solve the lemons problem.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.5P
Related questions
Question
Micro homework Q3
Please help to solve this
![Q3. Bayesian Games
An insurer sells insurance to a buyer who has private information about his own expected
loss. Without insurance, the buyer's payoff is -1.20, and it is common knowledge that 0 €
{2,4,6}, each type occurring with equal (1/3) probability. The insurer is better able to take
the loss and only suffers -0; for simplicity, the insurer is only able to offer a premium (flat
price of insurance) p, which the buyer can accept or reject. The insurer's rejection payoff is
0. If the offer is accepted, the insurer's payoff is p – 0, and the buyer's payoff is —p.
[I'll do the first part for you: Unconditional on anything, E[0] = } * 2 + ½ * 4 + } * 6 = 4.]
a. Prior to actually solving, explain in words what a "lemons problem" is and why this
qualifies.
b. For part (b) only, suppose that the insurer observes . Solve for the unique SPNE
in this game of perfect information; the answer will be in terms of 0.
c. Now solve for the (sequentially rational) BNE given the insurer doesn't observe 0.
d. Explain (in words) how a penalty (or a tax, if you're Justice Roberts) for refusing to
buy insurance could solve the lemons problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ceae03-ce82-43df-b816-3449c4a6aa24%2F61301208-5cf8-4384-b923-8344d8412bf3%2F3o2a0tw_processed.png&w=3840&q=75)
Transcribed Image Text:Q3. Bayesian Games
An insurer sells insurance to a buyer who has private information about his own expected
loss. Without insurance, the buyer's payoff is -1.20, and it is common knowledge that 0 €
{2,4,6}, each type occurring with equal (1/3) probability. The insurer is better able to take
the loss and only suffers -0; for simplicity, the insurer is only able to offer a premium (flat
price of insurance) p, which the buyer can accept or reject. The insurer's rejection payoff is
0. If the offer is accepted, the insurer's payoff is p – 0, and the buyer's payoff is —p.
[I'll do the first part for you: Unconditional on anything, E[0] = } * 2 + ½ * 4 + } * 6 = 4.]
a. Prior to actually solving, explain in words what a "lemons problem" is and why this
qualifies.
b. For part (b) only, suppose that the insurer observes . Solve for the unique SPNE
in this game of perfect information; the answer will be in terms of 0.
c. Now solve for the (sequentially rational) BNE given the insurer doesn't observe 0.
d. Explain (in words) how a penalty (or a tax, if you're Justice Roberts) for refusing to
buy insurance could solve the lemons problem.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Brief Principles of Macroeconomics (MindTap Cours…](https://www.bartleby.com/isbn_cover_images/9781337091985/9781337091985_smallCoverImage.gif)
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Essentials of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337091992/9781337091992_smallCoverImage.gif)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Brief Principles of Macroeconomics (MindTap Cours…](https://www.bartleby.com/isbn_cover_images/9781337091985/9781337091985_smallCoverImage.gif)
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Essentials of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337091992/9781337091992_smallCoverImage.gif)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning