Auctions are everywhere – on TV, in corporate boardrooms, all over the internet – and for just about everything, from trinkets and collectibles to natural resources and government contracts. Whether the stakes are silly or serious, auctions are an interesting combination of buying, selling, and gambling, all rolled into one.

In this lesson, students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.

- Calculate the probability of winning an auction with different bids distributed uniformly on an interval
- Write and graph functions that yield expected profit for various bids
- Find the vertex of a parabola in order to maximize expected profit from a quadratic function
- Develop and reason about higher-order polynomial expected value functions to maximize profit on an interval
- Make informal limit arguments about optimal biding strategy as the number of bidders in an auction increases

eBay, auctioneers everywhere

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