Podrobný výpis o publikaci

Combinatorial auctions are those auctions in which bidders can place bids on combinations of items. Solving of combinatorial auctions can be modeled by linear programming problems with using of duality theory. The paper is devoted to analyzing an iterative approach to solving combinatorial auctions. In the iterative approach, there are multiple rounds of bidding and allocation and the problem is solved in an iterative and incremental way. There is a connection between efficient auctions and duality theory. The primal-dual algorithm can be taken as a decentralized and dynamic method of determine the pricing equilibrium. A primaldual algorithm usually maintains a feasible dual solution and tries to compute a primal solution that is both feasible and satisfies the complementary slackness conditions. If such a solution is found, the algorithm terminates. Otherwise the dual solution is updated towards optimality and the algorithm continues with the next iteration. Several auction formats based on the primal-dual approach have been proposed.