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

This paper presents eMediator, an electronic commerce server prototype that demonstrates ways in which algorithmic support and game-theoretic incentive engineering can jointly improve the efficiency of ecommerce. eAuctionHouse, the configurable auction server, includes a variety of generalized combinatorial auctions and exchanges, pricing schemes, bidding languages, mobile agents, and user support for choosing an auction type. We introduce two new logical bidding languages for combinatorial markets: the XOR bidding language and the OR-of-XORs bidding language. Unlike the traditional OR bidding language, these are fully expressive. They therefore enable the use of the Clarke-Groves pricing mechanism for motivating the bidders to bid truthfully. eAuctionHouse also supports supply/demand curve bidding. eCommitter, the leveled commitment contract optimizer, determines the optimal contract price and decommitting penalties for a variety of leveled commitment contracting mechanisms, taking into account that rational agents will decommit strategically in Nash equilibrium. It also determines the optimal decommitting strategies for any given leveled commitment contract. eExchangeHouse, the safe exchange planner, enables unenforced anonymous exchanges by dividing the exchange into chunks and sequencing those chunks to be delivered safely in alternation between the buyer and the seller.

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