Mechanism design without quasilinearity

Abstract

This paper studies a model of mechanism design with transfers where agents' preferences need not be quasilinear. In such a model, (i) we characterize dominant strategy incentive compatible mechanisms using a monotonicity property, (ii) we establish a revenue uniqueness result (for every dominant strategy implementable allocation rule, there is a unique payment rule that can implement it), and (iii) we show that every dominant strategy incentive compatible, individually rational, and revenue-maximizing mechanism must charge zero payment for the worst alternative (outside option). These results are applicable in a wide variety of problems (single object auction, multiple object auction, public good provision, etc.) under suitable richness of type space. In particular, our results are applicable to two important type spaces: (a) type space containing an arbitrarily small perturbation of quasilinear type space and (b) type space containing all positive income effect preferences.

Mechanism Design for Unequal Societies

“…One of the earliest extensions of the standard quasilinear framework was Maskin and Riley [1984], who pin down the optimal auction in a setting with risk-averse buyers. Saitoh and Serizawa [2008], Hashimoto and Saitoh [2010], and Kazumura et al [2020] characterize, among others, the set of mechanisms that retain certain desiderata in nonquasilinear settings, such as the VCG features. Eisenhuth [2019] studies the revenuemaximizing auction when agents are loss averse and the reference point is endogenous to the choice of the mechanism.…”

Characterizing Pairwise Strategy-Proof Rules in Object Allocation Problems with Money

“…A rule revenue dominates another rule if for each preference profile, the revenue from the former rule is greater than or equal to that from the latter rule, and for some preference profile, the inequality is strict 6. Kazumura et al(2020) show that in a non-quasi-linear environment, the standard revenue equivalence approach is no longer valid, and the revenue maximization problem is no longer tractable even in a canonical one-object setting 7. Note that if a rule maximizes revenue in terms of standard expected revenues among a class of rules, then it is revenue undominated within the class of rules.…”