arXiv subjects

Andrew Chi-Chih Yao

Publications and source records attributed to Andrew Chi-Chih Yao.

22 records · Page 2Linked to original sources

arXiv2017

On Revenue Monotonicity in Combinatorial Auctions

Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for $m$ items and $n$ buyers in the Bayesian setting, specified by a valuation function $v$ and a set $F$ of $nm$ independent item-type distributions. Let $REV(v, F)$ denote the maximum revenue achievable under $F$ by any incentive compatible mechanism. Intuitively, one would expect that $REV(v, G)\geq REV(v, F)$ if distribution $G$ stochastically dominates $F$. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when $v$ is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions $v$, showing that $REV(v, G)\geq c\,REV(v, F)$ if $G$ stochastically dominates $F$ under $v$ where $c>0$ is a universal constant. Previously, approximate monotonicity was known only for the case $n=1$: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.

cs.GT↗

arXiv2016

On Solutions for the Maximum Revenue Multi-item Auction under Dominant-Strategy and Bayesian Implementations

Very few exact solutions are known for the monopolist's $k$-item $n$-buyer maximum revenue problem with additive valuation in which $k, n >1$ and the buyers $i$ have independent private distributions $F^j_i$ on items $j$. In this paper we derive exact formulas for the maximum revenue when $k=2$ and $F^j_i$ are any IID distributions on support of size 2, for both the dominant-strategy (DIC) and the Bayesian (BIC) implementations. The formulas lead to the simple characterization that, the two implementations have identical maximum revenue if and only if selling-separately is optimal for the distribution. Our results also give the first demonstration, in this setting, of revenue gaps between the two implementations. For instance, if $k=n=2$ and $Pr\{X_F=1\}=Pr\{X_F=2\}=\frac{1}{2}$, then the maximum revenue in the Bayesian implementation exceeds that in the dominant-strategy by exactly $2\%$; the same gap exists for the continuous uniform distribution $X_F$ over $[a, a+1]\cup[2a, 2a+1]$ for all large $a$.

cs.GT↗

arXiv2014

An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications

In this paper, we introduce a novel approach for reducing the $k$-item $n$-bidder auction with additive valuation to $k$-item $1$-bidder auctions. This approach, called the \emph{Best-Guess} reduction, can be applied to address several central questions in optimal revenue auction theory such as the power of randomization, and Bayesian versus dominant-strategy implementations. First, when the items have independent valuation distributions, we present a deterministic mechanism called {\it Deterministic Best-Guess} that yields at least a constant fraction of the optimal revenue by any randomized mechanism. Second, if all the $nk$ valuation random variables are independent, the optimal revenue achievable in {\it dominant strategy incentive compatibility} (DSIC) is shown to be at least a constant fraction of that achievable in {\it Bayesian incentive compatibility} (BIC). Third, when all the $nk$ values are identically distributed according to a common one-dimensional distribution $F$, the optimal revenue is shown to be expressible in the closed form $Θ(k(r+\int_0^{mr} (1-F(x)^n) \ud x))$ where $r= sup_{x\geq 0} \, x(1 - F(x)^n)$ and $m=\lceil k/n\rceil$; this revenue is achievable by a simple mechanism called \emph{2nd-Price Bundling}. All our results apply to arbitrary distributions, regular or irregular.

cs.GT↗

arXiv2014

Quantum replication at the Heisenberg limit

No process in nature can perfectly clone an arbitrary quantum state. But is it possible to engineer processes that replicate quantum information with vanishingly small error? Here we demonstrate the possibility of probabilistic super-replication phenomena where N equally prepared quantum clocks are transformed into a much larger number of M nearly perfect replicas, with an error that rapidly vanishes whenever M is small compared to the square of N. The quadratic replication rate is the ultimate limit imposed by Quantum Mechanics to the proliferation of information and is fundamentally linked with the Heisenberg limit of quantum metrology.

quant-ph↗