Lei Wang

Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions

Abstract— Applications in complex systems such as the Internet have spawned recent interest in studying situations involving multiple agents with their individual cost or utility functions. In this paper, we introduce an algorithmic framework for studying combinatorial problems in the presence of multiple agents with submodular cost functions. We study several fundamental covering problems (Vertex Cover, Shortest Path, Perfect Matching, and Spanning Tree) in this setting and establish tight upper and lower bounds for the approximability of these problems

Approximability of combinatorial problems with multi-agent submodular cost functions

Abstract— Applications in complex systems such as the Internet have spawned recent interest in studying situations involving multiple agents with their individual cost or utility functions. In this paper, we introduce an algorithmic framework for studying combinatorial problems in the presence of multiple agents with submodular cost functions. We study several fundamental covering problems (Vertex Cover, Shortest Path, Perfect Matching, and Spanning Tree) in this setting and establish tight upper and lower bounds for the approximability of these problems

Budget smoothing for internet ad auctions: a game theoretic approach

In Internet ad auctions, search engines often throttle budget constrained advertisers so as to spread their spends across the specified time period. Such policies are known as budget smoothing policies. In this paper, we perform a principled, game-theoretic study of what the outcome of an ideal budget smoothing algorithm should be. In particular, we propose the notion of regret-free budget smoothing policies whose outcomes throttle each advertiser optimally, given the participation of the other advertisers. We show that regret-free budget smoothing policies always exist, and in the case of single slot auctions we can give a polynomial time smoothing algorithm. Inspired by the existence proof, we design a heuristic for budget smoothing which performs considerably better than existing benchmark heuristics.

On the approximation ratio of k -lookahead auction

We consider the problem of designing a profit-maximizing single-item auction, where the valuations of bidders are correlated. We revisit the k-lookahead auction introduced by Ronen [6] and recently further developed by Dobzinski, Fu and Kleinberg [2]. By a more delicate analysis, we show that the k-lookahead auction can guarantee at least

Combinatorial Problems with Discounted Price Functions in Multi-agent Systems.

\frac{e^{1-1/k}}{e^{1-1/k}+1}

Continuity Properties of Equilibria in Some Fisher and Arrow-Debreu Market Models

of the optimal revenue, improving the previous best results of

Submodularity Helps in Nash and Nonsymmetric Bargaining Games

\frac{2k-1}{3k-1}

Efficiency, Fairness and Competitiveness in Nash Bargaining Games

in [2]. The 2-lookahead auction is of particular interest since it can be derandomized [2, 5]. Therefore, our result implies a polynomial time deterministic truthful mechanism with a ratio of

Single-parameter combinatorial auctions with partially public valuations

\frac{\sqrt{e}}{\sqrt{e}+1}

Optimal Approximation Algorithms for Multi-agent Combinatorial Problems with Discounted Price Functions

≈ 0.622 for any single-item correlated-bids auction, improving the previous best ratio of 0.6. Interestingly, we can show that our analysis for 2-lookahead is tight. As a byproduct, a theoretical implication of our result is that the gap between the revenues of the optimal deterministically truthful and truthful-in-expectation mechanisms is at most a factor of