Posted Price Clauses in Ascending Auctions

One most conspicuous and curious phenomenon in online auctions is that a large fraction of goods sold have posted price clauses whereby bidders can buy the goods without taking part in the auctions. Two types of posted price clauses exemplified by Amazon and eBay are found. The paper first develops a comprehensive theory of posted price auctions under various assumptions in auction theory. While the Amazon posted price is found to be an attractive innovation, the eBay posted price is generally dominated by either the Amazon posted price or the auction without posted price. This strikes us as a paradox as a dominated business model is offered by the largest online auction house. We next develop a more structural model for online auctions taking into account sequential arrivals of bidders. In this case, posted price clauses turn out to be more difficult to be a desirable selling device, hence resulting in a more general "posted price paradox." The last part of the paper offers a parsimonious theory that simultaneously resolves both the eBay and posted price paradoxes using the notion of bidder impatience that is a proxy of market competition.

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