Abstract
We consider a sequential location game on a continuous directional star network, where a finite number of players (facilities) sequentially choose their locations to serve their consumers who are uniformly and continuously distributed in the network. Each consumer patronizes all the closest locations that have been chosen, bringing them equal shares of payoff. In turn, each location distributes the total payoff it receives evenly to every player choosing it. We study hierarchical Stackelberg equilibria (HSE), a.k.a, subgame perfect equilibria of the game, under which every player chooses a location to maximize its payoff. We establish a universal lower bound for payoff to a player under any HSE outcome. The lower bound is then strengthened with better estimations, and some HSE outcomes are explicitly presented, provided that the number of players and the network parameters satisfy certain relations.
Research supported in part by NNSF of China under Grant No. 11531014.
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Notes
- 1.
In our discussion, all directional intervals are closed.
References
Anderson, S., Engers, M.: Stackelberg versus cournot oligopoly equilibrium. Int. J. Ind. Organ. 10, 127–135 (1992)
Prescott, E.C., Visscher, M.: Sequential location among firms with foresight. Bell J. Econ. 8, 378–393 (1977)
Cancian, M., Bills, A., Bergstrom, T.: Hotelling location problems with directional constraints: an application to television news scheduling. J. Ind. Econ. 43, 121–124 (1995)
Colombo, S.: Spatial price discrimination in the unidirectional hotelling model with elastic demand. J. Econ. 102(2), 157–169 (2011)
Colombo, S.: Spatial cournot competition with non-extreme directional constraints. Ann. Reg. Sci. 51, 761–774 (2013)
Drezner, Z.: Competitive location strategies for two facilities. Reg. Sci. Urban Econ. 12, 485–493 (1982)
Eiselt, H., Marianov, V.: Foundations of Location Analysis, vol. 155. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-7572-0
Fournier, G., Scarsini, M.: Hotelling games on networks: existence and efficiency of equilibria. Math. Oper. Res. 44, 212–235 (2016)
Gentile, J., Pessoa, A., Poss, M., Costa Roboredo, M.: Integer programming formulations for three sequential discrete competitive location problems with foresight. Eur. J. Oper. Res. 265, 872–881 (2017)
Gorji, M.: Competitive location: a state-of-art review. Int. J. Ind. Eng. Comput. 6, 1–18 (2015)
Hakimi, S.: On locating new facilities in a competitive environment. Eur. J. Oper. Res. 12, 29–35 (1983)
Hotelling, H.: Stability in competition. Econ. J. 39(153), 41–57 (1929)
Yates, A.J.: Hotelling and the new york stock exchange. Econ. Lett. 56, 107–110 (1997)
Kress, D.: Sequential Competitive Location on Networks (2013)
Lai, F.C.: Sequential locations in directional markets. Reg. Sci. Urban Econ. 31, 535–546 (2001)
San Martin, G., Cordera, R., Alonso, B.: Spatial Interaction Models (2017)
Sun, C.H.: Sequential location in a discrete directional market with three or more players. Ann. Reg. Sci. 48, 101–122 (2012)
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Chen, X., Hu, X., Zhang, M. (2020). Sequential Location Game on Continuous Directional Star Networks. In: Du, DZ., Wang, J. (eds) Complexity and Approximation. Lecture Notes in Computer Science(), vol 12000. Springer, Cham. https://doi.org/10.1007/978-3-030-41672-0_11
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DOI: https://doi.org/10.1007/978-3-030-41672-0_11
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