Name
Title | ||
|---|---|---|
Technical Note-The Competitive Facility Location Problem in a Duopoly: Advances Beyond Trees |
Abstract | ||
|---|---|---|
AbstractWe consider a competitive facility location problem on a network where consumers located on vertices wish to connect to the nearest facility. Knowing this, each competitor locates a facility on a vertex, trying to maximize market share. We focus on the two-player case and study conditions that guarantee the existence of a pure-strategy Nash equilibrium for progressively more complicated classes of networks. For general graphs, we show that attention can be restricted to a subset of vertices referred to as the central block. By constructing trees of maximal bi-connected components, we obtain sufficient conditions for equilibrium existence. Moreover, when the central block is a vertex or a cycle for example, in cactus graphs, this provides a complete and efficient characterization of equilibria. In that case, we show that both competitors locate their facilities in a solution to the 1-median problem, generalizing a well-known insight arising from Hotelling's model. We further show that an equilibrium must solve the 1-median problem in other classes of graphs, including grids, which essentially capture the topology of urban networks. In addition, when both players select a 1-median, the solution must be at equilibrium for strongly-chordal graphs, generalizing a previously known result for trees.The electronic companion is available at https://doi.org/10.1287/opre.2017.1694. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1287/opre.2017.1694 | Periodicals |
Keywords | Field | DocType |
competitive facility location,Hotelling competition,1-median,Nash equilibrium,Voronoi game | Duopoly,Mathematical optimization,Technical note,Vertex (geometry),Generalization,Facility location problem,Nash equilibrium,Market share,Mathematics,Competitor analysis | Journal |
Volume | Issue | ISSN |
66 | 4 | 0030-364X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yonatan Gur | 1 | 65 | 5.21 |
| Daniela Saban | 2 | 31 | 7.84 |
| Nicolás E. Stier Moses | 3 | 390 | 26.21 |