Auction Design and Optimal Allocation by Linear Programming
M.S. Thesis Presentation by Halil İbrahim Bayrak Department of Industrial Engineering Bilkent University
For the sale of a single object through an auction, we assume discrete type space for agents and make use of linear programming to find optimal mechanism design for a risk-neutral seller. First, we show that the celebrated incentive compatible mechanism, second price auction, is not optimal. We find a slightly different optimal mechanism referred to as “discrete second price auction”. Secondly we look at the problem of allocation with costly inspection. We obtain the optimal solution in the form of a favored-agent mechanism by the Greedy Algorithm. Lastly, we relax the common prior assumption and maximize the worst-case utility of an ambiguity averse seller for the two problems mentioned above. While the problem does not yield a useful optimal mechanism in general, optimal solutions for some special cases are obtained.
This thesis is supervised by Prof. Mustafa Ç. Pınar