Mechanism Design and Risk Aversion

TL;DR

This paper develops efficient algorithms for designing utility-maximizing mechanisms in Bayesian settings with risk-averse players, providing approximation guarantees and new computational techniques for multi-unit auctions.

Contribution

It introduces the first polynomial-time algorithms for constructing utility-maximizing mechanisms with risk-averse agents, including multi-unit auctions and settings with both risk-averse buyers and sellers.

Findings

Provides a $(1-1/e- ext{eps})$-approximate SPM for risk-averse seller

Designs a truthful-in-expectation mechanism with a $(1-1/e- ext{eps})^3$ approximation for risk-averse buyers and seller

Offers a polynomial-time algorithm for revenue maximization with risk-neutral seller and risk-averse buyers

Abstract

We develop efficient algorithms to construct utility maximizing mechanisms in the presence of risk averse players (buyers and sellers) in Bayesian settings. We model risk aversion by a concave utility function, and players play strategically to maximize their expected utility. Bayesian mechanism design has usually focused on maximizing expected revenue in a {\em risk neutral} environment, and no succinct characterization of expected utility maximizing mechanisms is known even for single-parameter multi-unit auctions. We first consider the problem of designing optimal DSIC mechanism for a risk averse seller in the case of multi-unit auctions, and we give a poly-time computable SPM that is $(1-1/e-\eps)$-approximation to the expected utility of the seller in an optimal DSIC mechanism. Our result is based on a novel application of a correlation gap bound, along with {\em splitting} and {\em merging} of random variables to redistribute probability mass across buyers. This allows us to reduce our problem to that of checking feasibility of a small number of distinct configurations, each of which corresponds to a covering LP. A feasible solution to the LP gives us the distribution on prices for each buyer to use in a randomized SPM. We next consider the setting when buyers as well as the seller are risk averse, and the objective is to maximize the seller's expected utility. We design a truthful-in-expectation mechanism whose utility is a $(1-1/e -\eps)^3$-approximation to the optimal BIC mechanism under two mild assumptions. Our mechanism consists of multiple rounds that processes each buyer in a round with small probability. Lastly, we consider the problem of revenue maximization for a risk neutral seller in presence of risk averse buyers, and give a poly-time algorithm to design an optimal mechanism for the seller.