Note: alt I0 A Bidding Mode Note: SiModel Let U1,U2 ng Model. formly distributed

Question

Note: alt I0 A Bidding Mode Note: SiModel Let U1,U2 ng Model. formly distributed o ccessive bids on an asset that you are trying to sell, and that you mut 10 A BiddingA be independent random vanables,each buted over the interval (0,11. These random variables represen successive bids on an asset that you must sell when the asset becomes worthless. As a strategy, you adogt ime t = 1, when the asset becomes worthless. As a strategy, you adopt a by t ret number 6, and you will accept the first offer that is greater than F sec example, you accept the second offer if UIS while U2 > . Suppose that the offers arrive according to a unit rte Poisson process (= 1).

Explanation / Answer

P(you sell the asset) may be derived from the Poisson distribution. Note that the rate is now * (1-) = 1 * (1-) = 1- rather than simply , as 1 - is the probability that Ui >=

Then, P(X >= 1) = 1 - P(0) = 1 - e -(1-) = 1 - e -1+

b) Then, if it is sold, the price will be uniformly distributed between and 1. The average value is (1+)/2

Then, we must maximize (1 - e -1+ )(1+)/2 = 1/2 + /2 - e -1+ /2 - e -1+ /2

Take the derivative with respect to

1/2 - e -1+ /2 - e -1+ /2 - e -1+/2

1/2 - e -1+ /2 - e -1+ /2 - e -1+/2 = 0

Multiply by 2

1 - 2e -1+  - e -1+ = 0

1 = (2+)(e -1+)

e = (2+)e

= 0.207932009125294 0.2079

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.