Abstract
In this chapter we introduce the reader to auctions where the seller offers more than one unit (multi-unit auctions).
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Notes
- 1.
For more details on the third-order statistic of a valuation profile, see Exercise 2.10, which analyzes how to find the cumulative distribution function of the k th-order statistic, its associated density function, its application to the case in which valuations are uniformly distributed, and how to obtain the expected value and variance of the kth-order statistic.
- 2.
See Exercise 2.9 for more details about the second-order statistic, its cumulative distribution function, density function, and its application to the case in which valuations are uniformly distributed.
- 3.
Recall that, in the case of a quadratic equation ax 2 + bx + c = 0, where coefficients a, b, and c are real numbers (not necessarily positive), the discriminant is △ = b 2 − 4ac. When the discriminant is positive, △ > 0, the roots of the quadratic equation are real numbers and different from each other. Graphically the quadratic equation crosses the x-axis at two different points. However, when the discriminant is zero, △ = 0, roots are real numbers and at least two of them coincide. Finally, if △ < 0, there is a conjugate pair of complex roots, graphically meaning that the quadratic equation lies above the x-axis.
References
Krishna, V. (2009). Auction theory (2nd ed.). Cambridge, MA: Academic Press.
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Choi, PS., Munoz-Garcia, F. (2021). Multi-Unit Auctions. In: Auction Theory. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-69575-0_8
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