Agent-Mediated Electronic Commerce. Designing Trading Strategies and Mechanisms for Electronic Markets by Sofia Ceppi Esther David Chen Hajaj Valentin Robu & Ioannis A. Vetsikas

Author:Sofia Ceppi, Esther David, Chen Hajaj, Valentin Robu & Ioannis A. Vetsikas
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Proof

Let be the cleared sell orders and let be the uncleared sell orders in the actual auction. The broker’s actual bid resulted in the acquisition of (though may be zero), so limit price p was high enough to match of its bid to . Since , this would also have been the case if it had bid instead of . Moreover, bidding would have been enough to match the remaining demand to . Thus, if the broker had bid instead of , the bid would have been fully cleared. A bid with a limit price , however, may not have been enough for some potential values of X. Limit price is not high enough to match all of to . This means that a quantity that is larger than , has to be matched to . It may be that the quantity of the last cleared buy order is less than , and the limit price of the second last cleared buy order is greater than . In that case, a bid would not have been fully cleared, so is the worst case limit price to have acquired Q.

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