A developer would like to build an amusement park in the midst of the Suzhou Industrial Park. In order to build this park, he must purchase all of the land in a specific 10-acre area. If he does not get all of this land, he cannot build the park. Nobody except the developer knows exactly how much he would be willing to pay for the land. All persons other than the developer believe that the probability that he is willing to pay at least $p for the land is G(p) = e-plk where k = 200,000. (c) The 10 separate owners recognize that if they could somehow coordinate their offers, they would make much larger expected total profits. They decide to use the Vickrey-Clarke-Groves (VCG) mechanism to do so. The VCG mechanism works as follows. Each individual states an amount 1 that the land is worth to him. All of the land will be offered to the developer at a price p that would maximize total profits of owners if each owner reports his actual value r; = V;. If the developer chooses to purchase the land, then each owner will receive an equal share of the sales price p. In addition to receiving this share if the sale is made, each owner will pay a tax that depends on his response r; and on the responses of the other owners in the following way. Person i will receive the amount equal to the sum of the expected profits of the other 9 owners, but must pay an amount equal to the maximum expected profits that would be received by the other owners if the price were chosen to maximize the expected total profits of these other owners. With this mechanism, the best strategy for each owner is to state his true value r; = v; . If each owner uses this best strategy, at what price will the land be offered to the developer? What is the probability that the developer will buy the land? A developer would like to build an amusement park in the midst of the Suzhou Industrial Park. In order to build this park, he must purchase all of the land in a specific 10-acre area. If he does not get all of this land, he cannot build the park. Nobody except the developer knows exactly how much he would be willing to pay for the land. All persons other than the developer believe that the probability that he is willing to pay at least $p for the land is G(p) = e-plk where k = 200,000. (c) The 10 separate owners recognize that if they could somehow coordinate their offers, they would make much larger expected total profits. They decide to use the Vickrey-Clarke-Groves (VCG) mechanism to do so. The VCG mechanism works as follows. Each individual states an amount 1 that the land is worth to him. All of the land will be offered to the developer at a price p that would maximize total profits of owners if each owner reports his actual value r; = V;. If the developer chooses to purchase the land, then each owner will receive an equal share of the sales price p. In addition to receiving this share if the sale is made, each owner will pay a tax that depends on his response r; and on the responses of the other owners in the following way. Person i will receive the amount equal to the sum of the expected profits of the other 9 owners, but must pay an amount equal to the maximum expected profits that would be received by the other owners if the price were chosen to maximize the expected total profits of these other owners. With this mechanism, the best strategy for each owner is to state his true value r; = v; . If each owner uses this best strategy, at what price will the land be offered to the developer? What is the probability that the developer will buy the land
