64 research outputs found
Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints
We study the efficiency of non-truthful auctions for auto-bidders with both
return on spend (ROS) and budget constraints. The efficiency of a mechanism is
measured by the price of anarchy (PoA), which is the worst case ratio between
the liquid welfare of any equilibrium and the optimal (possibly randomized)
allocation. Our first main result is that the first-price auction (FPA) is
optimal, among deterministic mechanisms, in this setting. Without any
assumptions, the PoA of FPA is which we prove is tight for any
deterministic mechanism. However, under a mild assumption that a bidder's value
for any query does not exceed their total budget, we show that the PoA is at
most . This bound is also tight as it matches the optimal PoA without a
budget constraint. We next analyze two randomized mechanisms: randomized FPA
(rFPA) and "quasi-proportional" FPA. We prove two results that highlight the
efficacy of randomization in this setting. First, we show that the PoA of rFPA
for two bidders is at most without requiring any assumptions. This
extends prior work which focused only on an ROS constraint. Second, we show
that quasi-proportional FPA has a PoA of for any number of bidders, without
any assumptions. Both of these bypass lower bounds in the deterministic
setting. Finally, we study the setting where bidders are assumed to bid
uniformly. We show that uniform bidding can be detrimental for efficiency in
deterministic mechanisms while being beneficial for randomized mechanisms,
which is in stark contrast with the settings without budget constraints
An auction-based market equilibrium algorithm for a production model
AbstractWe present an auction-based algorithm for computing market equilibrium prices in a production model, in which producers have a single linear production constraint, and consumers have linear utility functions. We provide algorithms for both the Fisher and Arrow–Debreu versions of the problem
User Response in Ad Auctions: An MDP Formulation of Long-Term Revenue Optimization
We propose a new Markov Decision Process (MDP) model for ad auctions to
capture the user response to the quality of ads, with the objective of
maximizing the long-term discounted revenue. By incorporating user response,
our model takes into consideration all three parties involved in the auction
(advertiser, auctioneer, and user). The state of the user is modeled as a
user-specific click-through rate (CTR) with the CTR changing in the next round
according to the set of ads shown to the user in the current round. We
characterize the optimal mechanism for this MDP as a Myerson's auction with a
notion of modified virtual value, which relies on the value distribution of the
advertiser, the current user state, and the future impact of showing the ad to
the user. Moreover, we propose a simple mechanism built upon second price
auctions with personalized reserve prices and show it can achieve a
constant-factor approximation to the optimal long term discounted revenue
Prior-Independent Auctions for Heterogeneous Bidders
We study the design of prior-independent auctions in a setting with
heterogeneous bidders. In particular, we consider the setting of selling to
bidders whose values are drawn from independent but not necessarily
identical distributions. We work in the robust auction design regime, where we
assume the seller has no knowledge of the bidders' value distributions and must
design a mechanism that is prior-independent. While there have been many strong
results on prior-independent auction design in the i.i.d. setting, not much is
known for the heterogeneous setting, even though the latter is of significant
practical importance. Unfortunately, no prior-independent mechanism can hope to
always guarantee any approximation to Myerson's revenue in the heterogeneous
setting; similarly, no prior-independent mechanism can consistently do better
than the second-price auction. In light of this, we design a family of
(parametrized) randomized auctions which approximates at least one of these
benchmarks: For heterogeneous bidders with regular value distributions, our
mechanisms either achieve a good approximation of the expected revenue of an
optimal mechanism (which knows the bidders' distributions) or exceeds that of
the second-price auction by a certain multiplicative factor. The factor in the
latter case naturally trades off with the approximation ratio of the former
case. We show that our mechanism is optimal for such a trade-off between the
two cases by establishing a matching lower bound. Our result extends to selling
identical items to heterogeneous bidders with an additional -factor in our trade-off between the two cases
The Power of Two-sided Recruitment in Two-sided Markets
We consider the problem of maximizing the gains from trade (GFT) in two-sided
markets. The seminal impossibility result by Myerson shows that even for
bilateral trade, there is no individually rational (IR), Bayesian incentive
compatible (BIC) and budget balanced (BB) mechanism that can achieve the full
GFT. Moreover, the optimal BIC, IR and BB mechanism that maximizes the GFT is
known to be complex and heavily depends on the prior. In this paper, we pursue
a Bulow-Klemperer-style question, i.e. does augmentation allow for
prior-independent mechanisms to beat the optimal mechanism? Our main result
shows that in the double auction setting with i.i.d. buyers and i.i.d.
sellers, by augmenting buyers and sellers to the market, the GFT of a
simple, dominant strategy incentive compatible (DSIC), and prior-independent
mechanism in the augmented market is least the optimal in the original market,
when the buyers' distribution first-order stochastically dominates the sellers'
distribution. Furthermore, we consider general distributions without the
stochastic dominance assumption. Existing hardness result by Babaioff et al.
shows that no fixed finite number of agents is sufficient for all
distributions. In the paper we provide a parameterized result, showing that
agents suffice, where is the probability that the buyer's
value for the item exceeds the seller's value
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