Abstract: | *You and someone else both want to purchase (1) a house, and (2) furniture. One house and one lot of furniture are being auctioned. To both you and your competitor, the house and furniture are complements -- you would be willing to pay more to acquire both of them than the sum of what you would pay for each of them, if you had to consume it alone. But the two auctions are entirely separate. You cannot place a joint bid for the furnished-house package. What will be the equilibrium bidding strategies in this competition? After reviewing the model of, and two solution methods for, a single (private-value, first-price) auction, one method based on formulating and solving an ordinary differential equation and the other taking a lattice-theoretic approach, I will outline the respective 2-dimensional generalizations to attack the complementary-auctions problem. Each of these attempts runs into a mathematical problem that needs to be solved.The focus of this talk is to introduce an active research area in economic theory that generates problems in applied mathematics, rather than to exposit completed results. The complementary-auction model is drawn from research in progress by my student, Wiroy Shin.* |