Mechanism Design with Approximate Valuations

In mechanism design, we replace the strong assumption that each player knows his own payoff type EXACTLY with the more realistic assumption that he knows it only APPROXIMATELY. Specifically, we study the classical problem of maximizing social welfare in single-good auctions when players know their true valuations only within a constant multiplicative factor d in (0,1). Our approach is deliberately non-Bayesian and very conservative: each player i only knows that his true valuation is one among finitely many values in a d-APPROXIMATE SET, Ki, and his true valuation is ADVERSARIALLY and SECRETLY chosen in Ki at the beginning of the auction. We prove tight upper and lower bounds for the fraction of the maximum social welfare achievable in our model, in either dominant or undominated strategies, both via deterministic and probabilistic mechanisms. The landscape emerging is quite unusual and intriguing

Knightian Auctions

We study single-good auctions in a setting where each player knows his own valuation only within a constant multiplicative factor \delta{} in (0,1), and the mechanism designer knows \delta. The classical notions of implementation in dominant strategies and implementation in undominated strategies are naturally extended to this setting, but their power is vastly different. On the negative side, we prove that no dominant-strategy mechanism can guarantee social welfare that is significantly better than that achievable by assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the fraction of the maximum social welfare achievable in undominated strategies, whether deterministically or probabilistically

Mechanism design with approximate types

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 117-119).In mechanism design, we replace the strong assumption that each player knows his own payoff type exactly with the more realistic assumption that he knows it only approximately: each player i only knows that his true type [theta]i; is one among a set [Kappa]i, and adversarially and secretly chosen in Ki at the beginning of the game. This model is closely related to the Knightian [20] notion of uncertainty in economics, but we consider it from purely mechanism design's perspective. In particular, we study the classical problem of maximizing social welfare in auctions when players know their true valuations only within a constant multiplicative factor [delta] [xi] (0,1). For single good auctions, we prove that no dominant-strategy mechanism can guarantee better social welfare than assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the social welfare achievable in undominated strategies, whether deterministically or probabilistically. For multiple-good auctions, we prove that all dominant-strategy mechanisms can guarantee only an exponentially small fraction of the maximum social welfare, and the celebrated VCG mechanism (which is no longer dominant-strategy) guarantees, in undominated strategies, at most a doubly exponentially small fraction. For general games beyond auctions, we provide definitional foundations for this new approximate-type model, and provide a universality result showing that all reasonable (including Bayesian or Knightian) models of type uncertainty are equivalent to our set-theoretic one, at least for the setting when the type space is "convex". This work was done in collaboration with Silvio Micali and Alessandro Chiesa.by Zeyuan Allen Zhu.S.M