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Injecting unique minima into random sets and applications to ”Inverse Auctions”
| Content Provider | Semantic Scholar |
|---|---|
| Author | Louchard, Guy Bruss, F. Thomas Ward, Mark Daniel |
| Copyright Year | 2009 |
| Abstract | Consider N balls that are distributed among V urns according to some distribution G. We do not see the outcome and now have to place one ball into one urn with the goal of maximizing the probability that it will be the left-most urn containing a single ball. How should we proceed? This is the urn-model translation of an interesting problem posed by an internetauction offered by a German real-estate company. In the real problem only V is known (upper-price limit), whereas neither G (the way in which participants choose their offer) nor N (number of offers) is known. We would like to make an offer in such a way to maximize the probability that it turns out to be the minimum of the random set of single offers. We face a two-sided problem. On the one side we would like to choose a model which is convincing in terms of the expected behaviour of participants. On the other side, we want to solve an optimization problem; that is, the model should also be tractable and allow for asymptotic expansions, leading to a computable algorithm. Our attack is based on arguing that G should be (essentially) geometric and that some information on E(N) (expectation of N) and V(N) (variance of N) can be obtained in practice. Under certain conditions on possible dependencies of G and N , we can give answers. Poissonization (namely, changing the number N ofballs from a fixed quantity into a random quantity with Poisson distribution and mean N) and dePoissonization (i.e. reconciling with the original model) play here an important role to make the answers explicit. |
| Starting Page | 1 |
| Ending Page | 19 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| Volume Number | 6 |
| Alternate Webpage(s) | http://www.stat.purdue.edu/~mdw/papers/paper013full.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
