15 research outputs found
A Dynamic Axiomatic Approach to First-Price Auctions
The first-price auction is popular in practice for its simplicity and
transparency. Moreover, its potential virtues grow in complex settings where
incentive compatible auctions may generate little or no revenue. Unfortunately,
the first-price auction is poorly understood in theory because equilibrium is
not {\em a priori} a credible predictor of bidder behavior.
We take a dynamic approach to studying first-price auctions: rather than
basing performance guarantees solely on static equilibria, we study the
repeated setting and show that robust performance guarantees may be derived
from simple axioms of bidder behavior. For example, as long as a loser raises
her bid quickly, a standard first-price auction will generate at least as much
revenue as a second-price auction. We generalize this dynamic technique to
complex pay-your-bid auction settings and show that progressively stronger
assumptions about bidder behavior imply progressively stronger guarantees about
the auction's performance.
Along the way, we find that the auctioneer's choice of bidding language is
critical when generalizing beyond the single-item setting, and we propose a
specific construction called the {\em utility-target auction} that performs
well. The utility-target auction includes a bidder's final utility as an
additional parameter, identifying the single dimension along which she wishes
to compete. This auction is closely related to profit-target bidding in
first-price and ascending proxy package auctions and gives strong revenue
guarantees for a variety of complex auction environments. Of particular
interest, the guaranteed existence of a pure-strategy equilibrium in the
utility-target auction shows how Overture might have eliminated the cyclic
behavior in their generalized first-price sponsored search auction if bidders
could have placed more sophisticated bids
Approximately Optimal Risk-Averse Routing Policies via Adaptive Discretization
Mitigating risk in decision-making has been a long-standing problem. Due to the mathematical challenge of its nonlinear nature, especially in adaptive decision-making problems, finding optimal policies is typically intractable. With a focus on efficient algorithms, we ask how well we can approximate the optimal policies for the difficult case of general utility models of risk. Little is known about efficient algorithms beyond the very special cases of linear (risk-neutral) and exponential utilities since general utilities are not separable and preclude the use of traditional dynamic programming techniques. In this paper, we consider general utility functions and investigate efficient computation of approximately optimal routing policies, where the goal is to maximize the expected utility of arriving at a destination around a given deadline. We present an adaptive discretization variant of successive approximation which gives an \error-optimal policy in polynomial time. The main insight is to perform discretization at the utility level space, which results in a nonuniform discretization of the domain, and applies for any monotone utility function
On the Uniqueness of Equilibrium in Atomic Splittable Routing Games
In routing games with infinitesimal players, it follows from well-known convexity arguments that equilibria exist and are unique. In routing games with atomic players with splittable flow, equilibria exist, but uniqueness of equilibria has been demonstrated only in limited cases: in two-terminal nearly parallel graphs, when all players control the same amount of flow, and when latency functions are polynomials of degree at most three. There are no known examples of multiple equilibria in these games. In this work, we show that in contrast to routing games with infinitesimal players, atomic splittable routing games admit multiple equilibria. We demonstrate this multiplicity via two specific examples. In addition, we show that our examples are topologically minimal by giving a complete characterization of the class of network topologies for which multiple equilibria exist. Our proofs and examples are based on a novel characterization of these topologies in terms of sets of circulations