Problem
Research questions and friction points this paper is trying to address.
consumer utility maximization
mechanism design
constant-factor approximation
unit-demand buyers
simple mechanisms
A Constant-Factor Approximation to Multidimensional Consumer Utility
🤖 AI Summary
This study addresses the challenge that simple mechanisms fail to guarantee constant-factor approximations in multidimensional consumer utility maximization. Focusing on multi-buyer settings with heterogeneous items, it proposes a Bayesian incentive-compatible (BIC) mechanism integrating posted pricing and free lotteries. By decoupling the contributions of pricing and lotteries to establish an upper bound on optimal utility, the approach leverages randomized auctions, competition resolution, and polynomial-time algorithms for efficient computation. This work provides the first proof that simple mechanisms can achieve constant-factor approximations in this domain. Specifically, it attains an approximation ratio of 5.67+ε under independent valuations and improves upon 3.164 for i.i.d. valuations, simultaneously ensuring computational efficiency and incentive compatibility.
📝 Abstract
Motivated by social services where consumers pay with non-transferable ordeals, we study mechanisms that maximize consumer utility for multiple unit-demand buyers and heterogeneous items whose values are drawn independently from known prior distributions. Prior work in utility maximization approximates social welfare and shows that the gap between optimal utility and social welfare is logarithmic. We resolve the question of whether simple mechanisms can guarantee a constant-factor approximation to optimal utility itself. Our mechanisms achieve a $(5.67+\varepsilon)$-approximation for general independent values, improving to $2e/(e-1)<3.164$ when values are i.i.d. Each buyer chooses their favorite option from posted item prices or free item lotteries, and contention resolution determines which buyers' requests are served; this is BIC, ex-post individually rational, and computable in polynomial time. Our main technical contribution is a general upper bound on the optimal ex-ante-constrained utility that separates the contributions captured by posted prices and free lotteries. These results establish a utility counterpart to the theory of simple, approximately revenue-optimal mechanisms.
Innovation
Methods, ideas, or system contributions that make the work stand out.
consumer utility maximization
constant-factor approximation
posted prices
free lotteries
contention resolution
🔎 Similar Papers
No similar papers found.
