We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply short-sighted best-response strategies. We ask: when can a black-box approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm's approximation factor on average over many iterations? We present a general reduction for a broad class of algorithms when agents minimize external regret. We also present a new mechanism for the combinatorial auction problem that attains an @math approximation on average when agents apply best-response dynamics.
@cite_10 study implementation of algorithms in undominated strategies, which is a relaxation of the dominant strategy truthfulness concept. They focus on a variant of the CA problem in which agents are assumed to have single-value'' valuations, and present a mechanism to implement such auctions in a multi-round fashion. By comparison, mechanisms in our proposed model solve each instance of an auction in a one-shot manner, and our solution concept assumes that the auction is repeated multiple times.
@cite_10
2142270691 1982492546 1622653397 2150582214
In this article, we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple the algorithmic allocation problem from the strategic aspects, by a procedure that converts any algorithm to a dominant-strategy ascending mechanism. This technique works for any single value domain, in which each agent has the same value for each desired outcome, and this value is the only private information. In particular, for “single-value CAs”, where each player desires any one of several different bundles but has the same value for each of them, our technique converts any approximation algorithm to a dominant strategy mechanism that almost preserves the original approximation ratio. Our second result provides the first computationally efficient deterministic mechanism for the case of single-value multi-minded bidders (with private value and private desired bundles). The mechanism achieves an approximation to the social welfare which is close to the best possible in polynomial time (unless PeNP). This mechanism is an algorithmic implementation in undominated strategies, a notion that we define and justify, and is of independent interest. This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multi-parameter agents. We focus on approximation algorithms for NP-hard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques.Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for single-minded multi-unit auctions. The best previous result for such auctions was a 2-approximation. In addition, we present a monotone PTAS for the generalized assignment problem with any bounded number of parameters per agent.The most efficient way to solve packing integer programs (PIPs) is LP-based randomized rounding, which also is in general not monotone. We show that primal-dual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like single-minded combinatorial auctions (CAs), unsplittable flow routing and multicast routing. Our approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle. This manuscript presents an alternative implementation of the truthful-in-expectation mechanism of Dughmi, Roughgarden and Yan for combinatorial auctions with weighted-matroid-rank-sum valuations. The new implementation uses only value queries and is approximately truthful-in-expectation, in the sense that by reporting truthfully each agent maximizes his utility within a multiplicative 1-o(1) factor. It still provides an optimal (1-1 e-o(1))-approximation in social welfare. We achieve this by first presenting an approximately maximal-in-distributional-range allocation rule and then showing a black-box transformation to an approximately truthful-in-expectation mechanism. We study a limited-supply online auction problem, in which an auctioneer has k goods to sell and bidders arrive and depart dynamically. We suppose that agent valuations are drawn independently from some unknown distribution and construct an adaptive auction that is nevertheless value- andtime-strategy proof. For the k=1 problem we have a strategyproof variant on the classic secretary problem. We present a 4-competitive (e-competitive) strategyproof online algorithm with respect to offline Vickrey for revenue (efficiency). We also show (in a model that slightly generalizes the assumption of independent valuations) that no mechanism can be better than 3 2-competitive (2-competitive) for revenue (efficiency). Our general approach considers a learning phase followed by an accepting phase, and is careful to handle incentive issues for agents that span the two phases. We extend to the k›1 case, by deriving strategyproof mechanisms which are constant-competitive for revenue and efficiency. Finally, we present some strategyproof competitive algorithms for the case in which adversary uses a distribution known to the mechanism.