Algorithm for combinatorial coalition formation and payoff division in an electronic marketplace

In an electronic marketplace, coalition formation allows buyers to enjoy a price discount for each item, and combinatorial auction enables buyers to place bids for a bundle of items that are complementary. Coalition formation and combinatorial auctions both help to improve the efficiency of a market, and they have received much attention from economists and computer scientists. But there has not been work studying the situations where both coalition formation and combinatorial auctions exist. In this paper we consider an e-market where each buyer places a bid on a combination of items with a reservation cost, and sellers offer price discounts for each item based on volumes. By artificially dividing the reservation cost of each buyer among the items, we can construct optimal coalitions with respect to each item. These coalitions satisfy the complementarity of the items by reservation cost transfers, and thus induce the optimal solution. We focus on the systems with linear price functions and present a polynomial-time algorithm to find a semi-optimal solution and a payoff division scheme that is in the core of the coalition. Simulation results show that the algorithm obtains a solution close to the optimal value.

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