Digital goods auction
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In auction theory, a digital goods auction is an auction in which a seller has an unlimited supply of a certain item.
A typical example is when a company sells a
If the valuations of all potential consumers are known, then the company faces a simple optimization problem - selecting the price that maximizes the profit. For concreteness, suppose there is a set of consumers and that they are ordered by their valuation, so that the consumer with the highest valuation (willing to pay the largest price for the movie) is called "1", the next-highest is called "2", etc. The valuation of consumer is denoted by , such that . For every , if the price is set to , then only the first consumers buy the movie, so the profit of the company is . It is clear that in this case, the company is best-off setting the price at exactly ; in this case its profit is . Hence, the company's optimization problem is:
The problem is that, usually, the valuations of the consumers are NOT known. The company can try to ask them, but then they will have an incentive to report lower valuations in order to decrease the price. There is a lot of research on designing
More details and references can be found there.