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4179. A Stackelberg location problem on the plane using delivered price equilibria
Invited abstract in session TC-61: Location with Multiple Actors, stream Locational Analysis.
Tuesday, 12:30-14:00Room: S10 (building: 101)
Authors (first author is the speaker)
| 1. | Boglárka G.-Tóth
|
| Department of Computational Optimization, University of Szeged | |
| 2. | Jose Fernandez
|
| Estadistica e Investigacion Operativa, Universidad de Murcia |
Abstract
We study the problem of finding the optimal location and price equilibria of a Stackelberg location game when price equilibria are used. First, the leader and then the follower choose their locations and then set delivered prices to maximise their profits. Previous work has solved problems of location-price equilibria on different settings, showing that the minimiser of the social cost gives a location equilibrium. Any solution to the Stackelberg problem is also a location equilibrium, and it can be shown that there are location equilibria which are not minimizers of the social cost. Our research question is whether there may exist a Stackelberg solution which is not an equilibrium provided by the social cost. Assuming that firms set the equilibrium prices after the locations are fixed, the problem can be modelled as a bilevel optimization problem. We propose an exact interval branch-and-bound algorithm, suitable for relatively small problems, to obtain rigorous solutions. Our main goal is to see how the Stackelberg solution can differ from the location-price equilibria provided by the minimization of the social cost.
Keywords
- Location
- Continuous Optimization
- Global Optimization
Status: accepted
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