Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

An Experimental Analysis of Ending Rules in Internet Auctions

A great deal of late bidding has been observed on internet auctions such as eBay, which employ a second price auction with a fixed deadline. Much less late bidding has been observed on internet auctions such as those run by Amazon, which employ similar auction rules, but use an ending rule that automatically extends the auction if necessary after the scheduled close until ten minutes have passed without a bid. This paper reports an experiment that allows us to examine the effect of the different ending rules under controlled conditions, without the other differences between internet auction houses that prevent unambiguous interpretation of the field data. We find that the difference in auction ending rules is sufficient by itself to produce the differences in late bidding observed in the field data. The experimental data also allow us to examine how individuals bid in relation to their private values, and how this behavior is shaped by the different opportunities for learning provided in the auction conditions.

Buy-It-Now prices in eBay Auctions - The Field in the Lab

Electronic commerce has grown extraordinarily over the years, with online auctions being extremely successful forms of trade. Those auctions come in a variety of different formats, such as the Buy-It-Now auction format on eBay, that allows sellers to post prices at which buyers can purchase a good prior to the auction. Even though, buyer behavior is well studied in Buy-It-Now auctions, as to this point little is known about how sellers set Buy-It-Now prices. We investigate into this question by analyzing seller behavior in Buy-It-Now auctions. More precisely, we combine the use of a real online auction market (the eBay platform and eBay traders) with the techniques of lab experiments. We find a striking link between the information about agents provided by the eBay market institution and their behavior. Information about buyers is correlated with their deviation from true value bidding. Sellers respond strategically to this information when deciding on their Buy-It-Now prices. Thus, our results highlight potential economic consequences of information publicly available in (online) market institutions

Buy-It-Now prices in eBay Auctions - The Field in the Lab

Electronic commerce has grown extraordinarily over the years, with online auctions being extremely successful forms of trade. Those auctions come in a variety of different formats, such as the Buy-It-Now auction format on eBay, that allows sellers to post prices at which buyers can purchase a good prior to the auction. Even though, buyer behavior is well studied in Buy-It-Now auctions, as to this point little is known about how sellers set Buy-It-Now prices. We investigate into this question by analyzing seller behavior in Buy-It-Now auctions. More precisely, we combine the use of a real online auction market (the eBay platform and eBay traders) with the techniques of lab experiments. We find a striking link between the information about agents provided by the eBay market institution and their behavior. Information about buyers is correlated with their deviation from true value bidding. Sellers respond strategically to this information when deciding on their Buy-It-Now prices. Thus, our results highlight potential economic consequences of information publicly available in (online) market institutions.electronic markets; experience; online auctions; BIN price; buyout

Buy-it-Now Prices in eBay Auctions-The Field in the Lab

This article is an experimental investigation on decision making in online auction markets. We focus on a widely used format, the Buy-It-Now auction on eBay, where sellers post prices at which buyers can purchase a good prior to an auction. Even though, buyer behavior is well studied in Buy-It-Now auctions, up to date little is known about the behavior of sellers. In this article, we study how sellers set Buy-It-Now prices by combining the use of a real online auction market (the eBay platform and eBay traders) with the techniques of lab experiments. We find a striking relation between information about agents provided by eBay and their behavior. Information about buyers is correlated with their deviation from true value bidding. Sellers respond strategically to this information when deciding on their Buy-It-Now prices. Our results highlight consequences of information publicly available in (online) markets and underline the crucial role of institutional details.Electronic markets, experience, online auctions, BIN price, buyout price, risk, single item auction, private value, experiment

Information Revelation in an Online Auction with Common Values

The Hard Close auction has become a familiar auction format in online markets and in a private value framework this dynamic second-price auction format has experimentally been tested in recent studies. Considering a common value framework, Bajari and Hortaçsu (2003) demonstrate that in the Hard Close auction format bidders, using a sniping strategy, do not provide information during the auction. We provide contrary results from a laboratory experiment. Bidders provide information during the bidding process, resulting in different bid functions that depend on the bidders private information rank.auctions, electronic markets, experiments

A comparison of Candle Auctions and Hard Close Auctions with Common Values

With this study, we contribute to the literature of auction design by presenting a new auction format: the Candle auction, a popular auction in the Middle Ages. Considering a common value framework, we theoretically and experimentally point out that the Candle auction, where bidding is allowed until a stochastic deadline, yields a better outcome to the seller than the Hard Close auction, the popular eBay online auction format.online auctions, market design, experimental economics, common value

General Bounds for Incremental Maximization

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value $k\in\mathbb{N}$ that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such an incremental solution, i.e., the worst ratio over all $k$ between the incremental solution after $k$ steps and an optimum solution of cardinality $k$. We define a large class of problems that contains many important cardinality constrained maximization problems like maximum matching, knapsack, and packing/covering problems. We provide a general $2.618$-competitive incremental algorithm for this class of problems, and show that no algorithm can have competitive ratio below $2.18$ in general. In the second part of the paper, we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step. This algorithm is known to be $1.58$-competitive for submodular objective functions, but it has unbounded competitive ratio for the class of incremental problems mentioned above. We define a relaxed submodularity condition for the objective function, capturing problems like maximum (weighted) ($b$-)matching and a variant of the maximum flow problem. We show that the greedy algorithm has competitive ratio (exactly) $2.313$ for the class of problems that satisfy this relaxed submodularity condition. Note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems.Comment: fixed typo

An incremental algorithm for uncapacitated facility location problem

We study the incremental facility location problem, wherein we are given an instance of the uncapacitated facility location problem (UFLP) and seek an incremental sequence of opening facilities and an incremental sequence of serving customers along with their fixed assignments to facilities open in the partial sequence. We say that a sequence has a competitive ratio of k, if the cost of serving the first ℓ customers in the sequence is at most k times the optimal solution for serving any ℓ customers for all possible values of ℓ. We provide an incremental framework that computes a sequence with a competitive ratio of at most eight and a worst-case instance that provides a lower bound of three for any incremental sequence. We also present the results of our computational experiments carried out on a set of benchmark instances for the UFLP. The problem has applications in multistage network planning

Approximation Algorithms for Stochastic k-TSP

This paper studies the stochastic variant of the classical k-TSP problem where rewards at the vertices are independent random variables which are instantiated upon the tour\u27s visit. The objective is to minimize the expected length of a tour that collects reward at least k. The solution is a policy describing the tour which may (adaptive) or may not (non-adaptive) depend on the observed rewards. Our work presents an adaptive O(log k)-approximation algorithm for Stochastic k-TSP, along with a non-adaptive O(log^2 k)-approximation algorithm which also upper bounds the adaptivity gap by O(log^2 k). We also show that the adaptivity gap of Stochastic k-TSP is at least e, even in the special case of stochastic knapsack cover