Matthew Cary

Greedy bidding strategies for keyword auctions

How should players bid in keyword auctions such as those used by Google, Yahoo! and MSN?allWe consider greedy bidding strategies for a repeated auction on a single keyword, where in each round, each player chooses some optimal bid for the next round, assuming that the other players merely repeat their previous bid. We study the revenue, convergence and robustness properties of such strategies. Most interesting among these is a strategy we call the balanced bidding strategy (BB): it is known that BB has a unique fixed point with payments identical to those of the VCG mechanism. We show that if all players use the BB strategy and update each round, BB converges when the number of slots is at most 2, but does not always converge for 3 or more slots. On the other hand, we present a simple variant which is guaranteed to converge to the same fixed point for any number of slots. In a model in which only one randomly chosen player updates each round according to the BB strategy, we prove that convergence occurs with probability 1.We complement our theoretical results with empirical studies.

Oblivious Hashing: A Stealthy Software Integrity Verification Primitive

We describe a novel software verification primitive called Oblivious Hashing. Unlike previous techniques that mainly verify the static shape of code, this primitive allows implicit computation of a hash value based on the actual execution (i.e., space-time history of computation) of the code. We also discuss its applications in local software tamper resistance and remote code authentication.

On profit maximization in mechanism design

Mechanism design is a subfield of game theory and microeconomics focused on incentive engineering. A mechanism is a protocol, typically taking the form of an auction, that is explicitly designed so that rational but non-cooperative agents, motivated solely by their self-interest, end up achieving the designers goals. The challenge of mechanism design is to apply these methods to traditional computer science goals such as worst-case or competitive analysis. We consider two challenging problems related to mechanism design for profit maximization: the analysis of natural bidding strategies used by participants in sponsored search auctions, and the design of a mechanism for matroid procurement with provable performance guarantees. The sponsored search auctions of web search engines such as Google or Yahoo! use the generalized second-price (GSP) mechanism, in which bidders do not have a dominant strategy. We develop a framework for studying a variety of greedy bidding strategies and analyze their revenue, convergence and robustness properties. We compare the performance of greedy bidding strategies to that of a Nash equilibrium, quantifying how close these bidding strategies are to one of the most natural and rational stable points of the system. In the procurement problem a buyer is given a set of agents with values, along with a family of feasible sets over the agents. The goal is to procure a feasible set of maximum value, for minimum cost. Assuming that a buyer obtains a decreasing marginal benefit per feasible set procured, the problem is to determine the optimal number of feasible sets to procure in order to maximize the buyers profit. We develop a mechanism that approximates the optimal profit to within a constant factor, when the set system is a matroid. Matroids are important structures in combinatorial optimization: for example, minimum spanning trees and node-weighted maximum matchings are both matroid problems. We also show that the well-known cost sharing revenue extraction mechanism is only truthful for matroid set systems, so that procurement problems over non-matroid set systems are not likely to be solved with current techniques.

Toward Optimal ε-Approximate Nearest Neighbor Algorithms

We combine the recent optimal predecessor algorithm with a recent randomized stratified tree algorithm for an ?-approximate nearest neighbor to give an algorithm for an ?-approximate nearest neighbor in a fixed-dimensional space that is optimal with respect to universe size. We also give a deterministic version of the stratified tree algorithm.

Convergence of Position Auctions under Myopic Best-Response Dynamics

We study the dynamics of multiround position auctions, considering both the case of exogenous click-through rates and the case in which click-through rates are determined by an endogenous consumer search process. In both contexts, we demonstrate that dynamic position auctions converge to their associated static, envy-free equilibria. Furthermore, convergence is efficient, and the entry of low-quality advertisers does not slow convergence. Because our approach predominantly relies on assumptions common in the sponsored search literature, our results suggest that dynamic position auctions converge more generally.

A Message Authentication Code Based on Unimodular Matrix Groups

We present a new construction based on modular groups. A novel element of our construction is to embed each input into a sequence of matrices with determinant ±1, the product of which yields the desired mac. We analyze using the invertibility and the arithmetic properties of the determinants of certain types of matrices; this may be of interest in other applications. Performance results on our preliminary implementations show the speed of our mac is competitive with recent fast mac algorithms, achieving 0.5 Gigabytes per second on a 1.06 GHz Celeron.

On the hardness of embeddings between two finite metrics

We improve hardness results for the problem of embedding one finite metric into another with minimum distortion. This problem is equivalent to optimally embedding one weighted graph into another under the shortest path metric. We show that unless P = NP, the minimum distortion of embedding one such graph into another cannot be efficiently approximated within a factor less than 9/4 even when the two graphs are unweighted trees. For weighted trees with the ratio of maximum edge weight to the minimum edge weight of α2 (α ≥ 1) and all but one node of constant degree, we improve this factor to 1+α. We also obtain similar hardness results for extremely simple line graphs (weighted). This improves and complements recent results of Kenyon et al.[13] and Papadimitriou and Safra [18].

The Long-Short-Key Primitive and Its Applications to Key Security

On todays open computing platforms, attackers can often extract sensitive data from a programs stack, heap, or files. To address this problem, we designed and implemented a new primitive that helps provide better security for ciphers that use keys stored in easily accessible locations. Given a particular symmetric key, our approach generates two functions for encryption and decryption: The short-key function uses the original key, while the functionally equivalent long-key version works with an arbitrarily long key derived from the short key. On common PC architectures, such a long key normally does not fit in stack frames or cache blocks, forcing an attacker to search memory space. Even if extracted from memory, the long key is neither easily compressible nor useful in recovering the short key. Using a pseudorandom generator and additional novel software-protection techniques, we show how to implement this construction securely for AES. Potential applications include white-box ciphers, DRM schemes, software smartcards, and challenge-response authentication, as well as any scenario where a key of controllable length is useful to enforce desired security properties.