Tuomas Sandholm

Coalition structure generation with worst case guarantees

Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.

Computing the optimal strategy to commit to

In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously.The recent surge in interest in computing game-theoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normal-form and Bayesian games. We give both positive results (efficient algorithms) and negative results (NP-hardness results).

Automated negotiation

tion engine then returns a list of products that satisfy all of the shopper’s hard constraints in order of how well they satisfy the shopper’s soft constraints. Tête-à-Tête uses comparable techniques to recommend complex products based on multiattribute utility theory. However, unlike PersonaLogic, Tête-à-Tête also assists buyers and sellers in the merchant-brokering and negotiation stages. Like PersonaLogic, Firefly (www.firefly.com) and other systems based on collaborative filtering [4] help consumers find products (see Figure 1). However, instead of filtering products based on features, Firefly recommends products through an automated “wordof-mouth” recommendation mechanism called “collaborative filtering.” The system first compares a shopper’s product ratings with those of other shoppers. After identifying the shopper’s “nearest neighbors,” or users with similar taste, the system recommends the products the neighbors rated highly but which the shopper may not yet have rated, possi-

Winner determination in combinatorial auction generalizations

Combinatorial markets where bids can be submitted on bundles of items can be economically desirable coordination mechanisms in multiagent systems where the items exhibit complementarity and substitutability. There has been a surge of research on winner determination in combinatorial auctions. In this paper we study a wider range of combinatorial market designs: auctions, reverse auctions, and exchanges, with one or multiple units of each item, with and without free disposal. We first theoretically characterize the complexity of finding a feasible, approximate, or optimal solution. Reverse auctions with free disposal can be approximated (even in the multi-unit case), although auctions cannot. When XOR-constraints between bids are allowed (to express substitutability), the hardness turns the other way around: even finding a feasible solution for a reverse auction or exchanges is &Ngr;&Pgr;-complete, while in auctions that is trivial. Finally, in all of the cases without free disposal, even finding a feasible solution is &Ngr;&Pgr;-complete.We then ran experiments on known benchmarks as well as ones which we introduced, to study the complexity of the market variants in practice. Cases with free disposal tended to be easier than ones without. On many distributions, reverse auctions with free disposal were easier than auctions with free disposal---as the approximability would suggest---but interestingly, on one of the most realistic distributions they were harder. Single-unit exchanges were easy, but multi-unit exchanges were extremely hard.

CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is \scr{N}\scr{P}-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster---especially in cases with structure. CABOBs search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem---the run-time distribution does not have a heavy tail.

eMediator : a next generation electronic commerce server

eMediator, a next generation electronic commerce server, demonstrates ways in which AI, algorithmic support, game theoretic incentive engineering, and GUI design can jointly improve the efficiency of ecommerce.The first component, eAuction House, is a configurable auction house that supports a large variety of parameterizable auction types. It supports generalized combinatorial auctions with new algorithms for winner determination. It also allows bidding via graphically drawn price-quantity graphs. It has an expert system for helping the user decide which auction type to use. Finally, it supports mobile software agents that bid optimally on the users behalf based on game theoretic analyses.The second component, eCommitter, is a leveled commitment contract optimizer. In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding. Leveled commitment contracts--i.e. contracts where each party can decommit by paying a predetermined penalty--were recently shown to improve Pareto efficiency even if agents rationally decommit in Nash equilibrium using inflated thresholds on how good their outside offers must be before they decommit. eCommitter solves the Nash equilibrium thresholds. Furthermore, it optimizes the contract price and decommitment penalties themselves.

Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges

In barter-exchange markets, agents seek to swap their items with one another, in order to improve their own utilities. These swaps consist of cycles of agents, with each agent receiving the item of the next agent in the cycle. We focus mainly on the upcoming national kidney-exchange market, where patients with kidney disease can obtain compatible donors by swapping their own willing but incompatible donors. With over 70,000 patients already waiting for a cadaver kidney in the US, this market is seen as the only ethical way to significantly reduce the 4,000 deaths per year attributed to kidney diseas. The clearing problem involves finding a social welfare maximizing exchange when the maximum length of a cycle is fixed. Long cycles are forbidden, since, for incentive reasons, all transplants in a cycle must be performed simultaneously. Also, in barter-exchanges generally, more agents are affected if one drops out of a longer cycle. We prove that the clearing problem with this cycle-length constraint is NP-hard. Solving it exactly is one of the main challenges in establishing a national kidney exchange. We present the first algorithm capable of clearing these markets on a nationwide scale. The key is incremental problem formulation. We adapt two paradigms for the task: constraint generation and column generation. For each, we develop techniques that dramatically improve both runtime and memory usage. We conclude that column generation scales drastically better than constraint generation. Our algorithm also supports several generalizations, as demanded by real-world kidney exchanges. Our algorithm replaced CPLEX as the clearing algorithm of the Alliance for Paired Donation, one of the leading kidney exchanges. The match runs are conducted every two weeks and transplants based on our optimizations have already been conducted.

Agents in Electronic Commerce: Component Technologies for Automated Negotiation and Coalition Formation

Automated negotiation and coalition formation among self-interested agents are playing an increasingly important role in electronic commerce. Such agents cannot be coordinated by externally imposing their strategies. Instead the interaction protocols have to be designed so that each agent is motivated to follow the strategy that the protocol designer wants it to follow. This paper reviews six component technologies that we have developed for making such interactions less manipulable and more efficient in terms of the computational processes and the outcomes: 1. OCSM-contracts in marginal cost based contracting, 2. leveled commitment contracts, 3. anytime coalition structure generation with worst case guarantees, 4. trading off computation cost against optimization quality within each coalition, 5. distributing search among insincere agents, and 6. unenforced contract execution. Each of these technologies represents a different way of battling self-interest and combinatorial complexity simultaneously. This is a key battle when multi-agent systems move into large-scale open settings.

Bargaining with deadlines

This paper analyzes automated distributive negotiation where agents have firm deadlines that are private information. The agents are allowed to make and accept offers in any order in continuous time. We show that the only sequential equilibrium outcome is one where the agents wait until the first deadline, at which point that agent concedes everything to the other. This holds for pure and mixed strategies. So, interestingly, rational agents can never agree to a nontrivial split because offers signal enough weakness of bargaining power (early deadline) so that the recipient should never accept. Similarly, the offerer knows that it offered too much if the offer gets accepted: the offerer could have done better by out-waiting the opponent. In most cases, the deadline effect completely overrides time discounting and risk aversion: an agents payoff does not change with its discount factor or risk attitude. Several implications for the design of negotiating agents are discussed. We also present an effective protocol that implements the equilibrium outcome in dominant strategies.

BOB: improved winner determination in combinatorial auctions and generalizations

Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary or substitutable. Determining the winners is NP- complete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper presents a more sophisticated search algorithm for optimal (and anytime) winner determination, including structural improvements that reduce search tree size, faster data structures, and optimizations at search nodes based on driving toward, identifying and solving tractable special cases. We also uncover a more general tractable special case, and design algorithms for solving it as well as for solving known tractable special cases substantially faster. We generalize combinatorial auctions to multiple units of each item, to reserve prices on singletons as well as combinations, and to combinatorial exchanges. All of these generalizations support both complementarity and substitutability of the items. Finally, we present algorithms for determining the winners in these generalizations.