代做ECON30290 - AUCTIONS AND MECHANISM DESIGN ASSIGNMENT 2代做迭代

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ECON30290 - AUCTIONS AND MECHANISM DESIGN

ASSIGNMENT 2

First Published: 12 March 2024

Online Answer Sheet Available: Noon, 22 April 2024

1. Instructions

a. No extensions will be given! Please set aside some time in advance to solve this assignment. You have been given over a month to do so.

c. Do not round answers while solving a problem. Only do so when you submit your answer.

e. When you submit your final answer include up to 3 digits after the decimal point and round down. Furthermore, do not include redundant zeros. For example 1/3 should be 0.333, √ 7 = 2.645, and 1/4 should be 0.25 (not 0.250).

2. Mechanism Design

1. There are 2 buyers i = 1, 2. The valuations are given by the CDFs F1(x) = x in [0, 1] and F2(x) = 2/x in [0, 2]. The seller wishes to find the optimal selling mechanism.

1.1 The function ψi is given by ψi(x) = Aix+Bi . Find A1, B1, A2, B2. (30 marks)

1.2 The optimal allocation can be described as follows:

• x1 < C1 and x2 < C2 ⇒ item isn’t sold.

• x1 ≥ D1 and x1 − x2 > D2 ⇒ buyer 1 wins.

• x2 > E1 and x2 − x1 > E2 ⇒ buyer 2 wins.

Find C1, C2, D1, D2, E1, E2. (45 marks)

1.3 The optimal payment functions are

Find F, G, H, I, J, K. (25 marks)