Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices
We show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences ca...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2022
|
| _version_ | 1811139297961574400 |
|---|---|
| author | Baldwin, E Bichler, M Fichtl, M Klemperer, P |
| author_facet | Baldwin, E Bichler, M Fichtl, M Klemperer, P |
| author_sort | Baldwin, E |
| collection | OXFORD |
| description | We show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments. |
| first_indexed | 2024-03-07T07:39:37Z |
| format | Journal article |
| id | oxford-uuid:9cec01af-7ca6-404e-95df-2fdbb39f8cc2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:03:51Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:9cec01af-7ca6-404e-95df-2fdbb39f8cc22024-05-16T09:05:08ZStrong substitutes: structural properties, and a new algorithm for competitive equilibrium pricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9cec01af-7ca6-404e-95df-2fdbb39f8cc2EnglishSymplectic ElementsSpringer2022Baldwin, EBichler, MFichtl, MKlemperer, PWe show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments. |
| spellingShingle | Baldwin, E Bichler, M Fichtl, M Klemperer, P Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title | Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title_full | Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title_fullStr | Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title_full_unstemmed | Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title_short | Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices |
| title_sort | strong substitutes structural properties and a new algorithm for competitive equilibrium prices |
| work_keys_str_mv | AT baldwine strongsubstitutesstructuralpropertiesandanewalgorithmforcompetitiveequilibriumprices AT bichlerm strongsubstitutesstructuralpropertiesandanewalgorithmforcompetitiveequilibriumprices AT fichtlm strongsubstitutesstructuralpropertiesandanewalgorithmforcompetitiveequilibriumprices AT klempererp strongsubstitutesstructuralpropertiesandanewalgorithmforcompetitiveequilibriumprices |