# CSCE 782: Problem Set 8

## Due: 12 December 2000

This is an extra-credit problem set.

Problem 1 (30%):

1. What is the dominant strategy in an English private value auction?
2. What is the dominant strategy in an English common value auction?
3. What is the dominant strategy in a first-price sealed bid private-value auction?
4. What is the dominant strategy in a first-price sealed-bid common-value auction?
5. What is the revenue difference between a first-price sealed-bid auction and a Dutch auction?

Problem 2 (30%): If the long distance companies offered to bid money to place each one of your long distance calls (after you tell them the number you want to call), which type of auction would provide the best incentive for them to continue to improve their technologies and lower their cost (thereby lowering the amount you pay)? why?

Problem 3 (40%): Two agents are trying to decide how to split a dollar bill. Agent 1 makes an offer, then 2 counter offers, then 1 counter-counter offers, and so on. (Assume we are using strategic bargaining theory to solve this).

1. If they can only do this for four rounds, what is the final outcome?
2. If they can only do this for five rounds, what is the final outcome?
3. If the dollar loses .2 of its value (i.e., it is worth 1, .8, .64, ...) what is the final outcome after four rounds?
4. If the dollar loses .2 of its value (i.e., it is worth 1, .8, .64, ...) what is the final outcome after an infinite number of rounds?

Jose M. Vidal