Thesis Proposal

 

"Mechanism Design with Convex Costs"

Takehiro Oyakawa

Tuesday, May 22, 2018 at 2:00 P.M.

Room 368 (CIT 3rd Floor)

Mechanisms are often designed with linear costs in mind. Under this assumption, many auction environments have been analyzed. However, we know that in many settings, costs are not linear, and can be better thought of as convex. For example, when a bidder in an auction must take out a loan to pay the auctioneer, the total amount of money the bidder must pay in the end often depends on a non-linearly increasing interest rate. Similarly, in contest settings, an agent's submission depends on the amount of effort exerted; here, a linear cost function does not capture diminishing returns.

In this proposal, we first describe mechanisms that capture convex cost settings. We analyze two such cases: a forward, direct setting, in which agents submit private information to the center, which describes their type, and a reverse, indirect setting, in which agents submit a payment to the center, based on their type. In particular, we study auctions and contest in single-parameter environments. We then show how one can quickly, and pragmatically, compute expected allocations and payments using perturbations. We propose to extend our analysis by analyzing how we can extend our perturbation methods beyond the single good setting. Next, we propose to analyze how randomly-sampled elements from a distribution can be used in our mechanisms. Finally, we propose using reinforcement learning to see how well an agent can learn to play in various settings.

Host: Professor Amy Greenwald