Synergies and Price Trends in Sequential Auctions
In this paper we consider sequential auctions where an individual's value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies in declining expected prices. There are several corollaries. First, the seller is indifferent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. When synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the first object is never exercised in the symmetric equilibrium and the seller's revenue in unchanged. Finally, we examine two special cases with asymmetric players. In the first case, players have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline. In the second case, one player wants two objects and the remaining players want one object each. For this example, we show that expected prices may not necessarily decrease as predicted by Branco (1997). The reason is that players with single-unit demand will generally bid less than their true valuations in the first period. Therefore, there are two opposing forces; the reduction in the bid of the player with multiple-demand in the last auction and less aggressive bidding in the first auction by the players with single-unit demand.
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