Distributed clusters like the Grid and PlanetLab enable the same statistical multiplexing efficiency gains for computing as the Internet provides for networking. One major challenge is allocating resources in an economically efficient and low-latency way. A common solution is proportional share, where users each get resources in proportion to their pre-defined weight. However, this does not allow users to differentiate the value of their jobs. This leads to economic inefficiency. In contrast, systems that require reservations impose a high latency (typically minutes to hours) to acquire resources. We present Tycoon, a market based distributed resource allocation system based on proportional share. The key advantages of Tycoon are that it allows users to differentiate the value of their jobs, its resource acquisition latency is limited only by communication delays, and it imposes no manual bidding overhead on users. We present experimental results using a prototype implementation of our design. 1

We study a class of single-round, sealed-bid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of the profit of optimal fixed pricing for all inputs. We justify the use of optimal fixed pricing as a benchmark for evaluating competitive auction profit. We show that several randomized auctions are truthful and competitive and that no truthful deterministic auction is competitive. Our results extend to bounded supply markets, for which we also get truthful and competitive auctions.

For allocation problems with one or more items, the wellknown Vickrey-Clarke-Groves (VCG) mechanism is efficient, strategy-proof, individually rational, and does not incur a deficit. However, the VCG mechanism is not (strongly) budget balanced: generally, the agents ’ payments will sum to more than 0. If there is an auctioneer who is selling the items, this may be desirable, because the surplus payment corresponds to revenue for the auctioneer. However, if the items do not have an owner and the agents are merely interested in allocating the items efficiently among themselves, any surplus payment is undesirable, because it will have to flow out of the system of agents. In 2006, Cavallo [3] proposed a mechanism that redistributes some of the VCG payment back to the agents, while maintaining efficiency, strategy-proofness, individual rationality, and the

In this paper we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to match without knowing what bids will arrive in the future. For maximizing profit, we present a (randomized) online algorithm with a competitive ratio of ln(p max min )+1, when bids are in a range [p min ,p max ], which we show is the best possible. A simpler algorithm has a ratio twice this, and can be used even if expiration times are not known. For maximizing the number of trades, we present a simple greedy algorithm that achieves a factor of 2 competitive ratio if no money-losing trades are allowed. Interestingly, we show that if the online algorithm is allowed to subsidize matches --- match money-losing pairs if it has already collected enough money from previous pairs to pay for them --- then it can be 1-competitive with respect to the optimal offline algorithm that is not allowed subsidy. That is, the ability to subsidize is at least as valuable as knowing the future. We also consider the objectives of maximizing buy or sell volume, and present algorithms that achieve a competitive ratio of 2(ln(p max /p min ) + 1), or ln(p max /p min ) + 1 if the online algorithm is allowed subsidization. We show the latter is the best possible competitive ratio for this setting. For social welfare maximization we also obtain an optimal competitive ratio, which is below ln(p max /p min ). We present all of these results as corollaries of theorems on online matching in an incomplete interval graph.

While market-based systems have long been proposed as solutions for distributed resource allocation, few have been deployed for production use in real computer systems. Towards this end, we present our initial experience using Mirage, a microeconomic resource allocation system based on a repeated combinatorial auction. Mirage allocates time on a heavilyused 148-node wireless sensor network testbed. In particular, we focus on observed strategic user behavior over a fourmonth period in which 312,148 node hours were allocated across 11 research projects. Based on these results, we present a set of key challenges for market-based resource allocation systems based on repeated combinatorial auctions. Finally, we propose refinements to the system’s current auction scheme to mitigate the strategies observed to date and also comment on some initial steps toward building an approximately strategyproof repeated combinatorial auction. 1

Consider a multi-agent system in a dynamic and uncertain environment. Each agent’s local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent’s MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multiagent variant of the multi-armed bandit problem is obtained as a special case. 1

Online mechanism design considers the problem of sequential decision making in a multi-agent system with self-interested agents. The agent population is dynamic and each agent has private information about its value for a sequence of decisions. We introduce a method (“ironing”) to transform an algorithm for online stochastic optimization into one that is incentivecompatible. Ironing achieves this by canceling decisions that violate a form of monotonicity. The approach is applied to the Consensus algorithm and experimental results in a resource allocation domain show that not many decisions need to be canceled and that the overhead of ironing is manageable.

Abstract. We give a simple analysis of the competitive ratio of the random sampling auction from [10]. The random sampling auction was first shown to be worst-case competitive in [9] (with a bound of 7600 on its competitive ratio); our analysis improves the bound to 15. In support of the conjecture that random sampling auction is in fact 4-competitive, we show that on the equal revenue input, where any sale price gives the same revenue, random sampling is exactly a factor of four from optimal. 1 Introduction. Random sampling is the most prevalent technique for designing auctions to maximize the auctioneer’s profit when the bidders ’ valuations are a priori unknown [2–4, 7, 8, 10, 11]. The first and simplest application of random sampling to auctions is in the context of auctioning a digital good. 5 For this problem, the random

Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many real-world applications (such as online ticket sales), the opposite is true: the seller has distributional knowledge of the bid values (e.g., via the history of past transactions in the market), but there is uncertainty about market size. Adopting the perspective of automated mechanism design, introduced by Conitzer and Sandholm, we develop algorithms that compute an optimal, or approximately optimal, online auction mechanism given access to this distributional knowledge. Our main results are twofold. First, we show that when the seller does not know the market size, no constant-approximation to the optimum efficiency or revenue is achievable in the worst case, even under the very strong assumption that bid values are i.i.d. samples from a distribution known to the seller. Second, we show that when the seller has distributional knowledge of the market size as well as the bid values, one can do well in several senses. Perhaps most interestingly, by combining dynamic programming with prophet inequalities (a technique from optimal stopping theory) we are able to design and analyze online mechanisms which are temporally strategyproof (even with respect to arrival and departure times) and approximately efficiency(revenue)-maximizing. In exploring the interplay between automated mechanism design and prophet inequalities, we prove new prophet inequalities motivated by the auction setting.

Appropriate abstractions, mechanisms, and policies for resource allocation is quickly emerging as the fundamental problem facing emerging computation and communication environments such as PlanetLab and the Grid. This paper explores the utility of one simple abstraction for global resource allocation with a number of appealing properties: a centralized auction that collects user descriptions of resource configurations and the values placed on these configurations. The task of the clearinghouse is to determine a set of winning bids and to assign appropriate subsets of global resources to individual users. One challenge with this model is the computational complexity associated with determining winners. To make the problem tractable, we propose appropriate bidding languages that constrain the type of bids that users can make, while maintaining required expressiveness. Computing optimal solutions to such auctions for scales of current interest (e.g., 1000 nodes) is intractable on current hardware, even given aggressive optimizations. Thus, we introduce a number of heuristics that appear to perform well in practice. Another challenge with auctions is the lag in clearing the auction and the uncertainty in whether resources will actually be acquired. We introduce a formulation for "Buy it Now" pricing to address some of these limitations.