ECON 479 Assignment 2 Write carefully your answers. Be concise (don't write a novel). 10% of the grade will be related to the quality of your writing. Question 1 (25 points) We have three bidders (A, B and C) and three goods (as, y and z). The valuations are: v43) = 160 1.113(3) = 120 \"00(3) = 40 v.4(y) = 80 1J3(y) = 140 vc(y) = 60 vA(z) = 0 153(2) = 0 00(2) = 200 vA(:ry) = 320 133(my) = 240 120(222) = 0 113(32) = 140 1:3(mz) = 100 000539) = 180 All the valuations that are missing are assumed to be equal to 0 (so for instance we have vA(myz) = 0, wall) = 0 for any bidder i = A, B, C, etc). Find the allocation and the price paid by each bidder with the VCG auction. Question 2 (15 points) We consider ads for a keyword. The search engine offers 2 links. The rst link has a frequency of 350 clicks / day, and the second link a click frequency of 290 clicks/day. There are 2 bidders, A and B. Bidder A values the click at $6 and bidder B values the click at $4. Consider the following assignment: bidder A gets the rst position and pays $3] click, while bidder B gets the second position and pays $1.5/click. Is this assignment stable? If not, identify a blocking pair (and explain why it is a blocking pair). If yes, justify your answers. Question 3 (15 points) We consider ads for a keyword. The search engine offers 2 links. The rst link has a. frequency of 700 clicks / day, and the second link a click frequency of 360 clicks/day. There are 2 bidders, A and B. Bidder A values the click at $6 and bidder B values the click at $4. Consider the following assignment: bidder A gets the rst position and pays $3/click, while bidder B gets the second position and pays $1.5/click. Is this assignment stable? If not, identify a blocking pair (and explain why it is a blocking pair). If yes, justify your answers. Question 4 (25 points) We consider ads for a keyword. The search engine offers 2 links. The rst link has a frequency of 100 clicks/ day, and the second link a click frequency of 40 clicks/day. There are 3 bidders, Alice, Bob and Carol. Alice values the click at $10, Bob values the click at $5, and Carol values the click at $1. We run the VCG auction. 1. Find the outcome of the auction (who gets which position). 1 2. How much each bidder pays to the search engine per week? 3. Does one of the agents have an incentive to rnjsreport their values? Explain. Question 5 (20 points) We have the assignment {Buyer 1, Seller 1), (Buyer 2, Seller 2). The payoffs are Buyer 1 Seller 1 Buyer 2 Seller 2 10 15 9 6 Buyer 1 and Seller 2 can generate together 15. Buyer 2 and Seller 1 can generate together 25. Is the assignment stable
