### Benjamin Brooks, University of Chicago

#### "A Strong Minimax Theorem for Informationally-Robust Auction Design"

16 Marzo 2021 - 15:30 hrs.

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Abstract: We study the design of profit-maximizing mechanisms in environments with interdependent values. A single unit of a good is for sale. There is a known joint distribution of the bidders’ ex post values for the good. Two programs are considered: (i) Maximize over mechanisms the minimum over information structures and equilibria of expected profit; (ii) Minimize over information structures the maximum over mechanisms and equilibria of expected profit. These programs are shown to have the same optimal value, which we term the profit guarantee. In addition, we characterize a family of linear programs that relax (i) and produce, for any finite number of actions, a mechanism with a corresponding lower bound on equilibrium profit. An analogous family of linear programs relax (ii) and produce, for any finite number of signals, an information structure with a corresponding upper bound on equilibrium profit. These lower and upper bounds converge to the profit guarantee as the numbers of actions and signals grow large. Our model can be extended to allow for demand constraints, multiple goods, and ambiguity about the value distribution. We report numerical simulations of approximate solutions to (i) and (ii).