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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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