Prior-independent auctions for risk-averse agents

Abstract

We study simple and approximately optimal auctions for agents with a particular form of risk-averse preferences. We show that, for symmetric agents, the optimal revenue (given a prior distribution over the agent preferences) can be approximated by the first-price auction (which is prior independent), and, for asymmetric agents, the optimal revenue can be approximated by an auction with simple form. These results are based on two technical methods. The first is for upper-bounding the revenue from a risk-averse agent. The second gives a payment identity for mechanisms with pay-your-bid semantics.

Optimal auctions for correlated buyers with sampling

“…Recently, several prior-independent auctions were studied [e.g. 8,19,10]. These auctions greatly reduce the amount or precision of the knowledge needed by the auctioneer on the prior distribution, while guaranteeing nearly optimal performance against the fully knowledgeable optimal auction.…”

Optimal Auctions vs. Anonymous Pricing

“…The utility function u is a concave function mapping from the wealth of an agent to a utility. Specifically, we restrict attention to a very specific form of risk aversion studied in Fu et al (2013), which is both computationally and analytically tractable: utility functions that are linear up to a given capacity C and then flat. Given allocation x and payment p, an agent has utility min{vx − p, C}.…”

“…In this section, we consider the case when agents are risk averse. Specifically, we consider the risk aversion model in Fu et al (2013), where each agent's utility function has a capacity constraint. Moreover, following Fu et al (2013), in this section, we consider the mechanisms that are pointwise individual rational, i.e., losers have no payment, and winners pay at most their reported values.…”

“…We introduce a definition and two lemmas, which are adapted from Fu et al (2013). Let (·) + = max{·, 0}.…”

On-Demand or Spot? Selling the Cloud to Risk-Averse Customers

“…Note also that for twicedifferentiable utility curves, u is more risk-averse than u * if and only if the standard Arrow-Pratt measure of risk-averson is nowhere lower for curve u than for curve u * [14]. 6 Demand structure Types are distributed according to a joint distribution F on pairs (v, u). For ease of exposition, we will assume throughout that F is supported on a finite collection of (v, u) pairs.…”