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Recent spectrum auctions in the United Kingdom, and some proposals for futureauctions of spectrum in the United States, are based on preliminary pricediscovery rounds, followed by calculation of final prices for the winningbuyers. For example, the prices could be the projection of Vikrey prices ontothe core of reported prices. The use of Vikrey prices should lead to morestraightforward bidding, but the projection reverses some of the incentive forbidders to report truthfully. Still, we conjecture that the price paid by awinning buyer increases no faster than the bid, as in a first price auction. Itwould be rather disturbing if the conjecture is false. The conjecture isestablished for a buyer interacting with disjoint groups of other buyers in astar network setting. It is also shown that for any core-selecting payment ruleand any integer w greater than or equal to two, there is a market setting withw winning buyers such that the price paid by some winning buyer increases atleast (1-1/w) times as fast as the price bid.

On the Incentive to Deviate in Core Selecting Combinatorial Auctions