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Robust equilibria in location games

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  • Buechel, Berno
  • Roehl, Nils

Abstract

In the framework of spatial competition, two or more players strategically choose a location in order to attract consumers. It is assumed standardly that consumers with the same favorite location fully agree on the ranking of all possible locations. To investigate the necessity of this questionable and restrictive assumption, we model heterogeneity in consumers’ distance perceptions by individual edge lengths of a given graph. A profile of location choices is called a “robust equilibrium” if it is a Nash equilibrium in several games which differ only by the consumers’ perceptions of distances. For a finite number of players and any distribution of consumers, we provide a complete characterization of robust equilibria and derive structural conditions for their existence. Furthermore, we discuss whether the classical observations of minimal differentiation and inefficiency are robust phenomena. Thereby, we find strong support for an old conjecture that in equilibrium firms form local clusters.

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  • Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
  • Handle: RePEc:eee:ejores:v:240:y:2015:i:2:p:505-517
    DOI: 10.1016/j.ejor.2014.07.019
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    1. Martin J. Osborne, 1995. "Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 261-301, May.
    2. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    3. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 27-49.
    4. Kelvin Lancaster, 1990. "The Economics of Product Variety: A Survey," Marketing Science, INFORMS, vol. 9(3), pages 189-206.
    5. Nilssen, Tore, 1997. "Sequential location when transportation costs are asymmetric," Economics Letters, Elsevier, vol. 54(2), pages 191-201, February.
    6. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    7. Braid, Ralph M., 2006. "The equilibrium locations of three stores with different selections of differentiated products," Economics Letters, Elsevier, vol. 93(1), pages 31-36, October.
    8. P. Hansen & J.-F. Thisse & R. E. Wendell, 1986. "Equivalence of Solutions to Network Location Problems," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 672-678, November.
    9. Wendell, R. E. & McKelvey, R. D., 1981. "New perspectives in competitive location theory," European Journal of Operational Research, Elsevier, vol. 6(2), pages 174-182, February.
    10. Byong-Duk Rhee, 1996. "Consumer Heterogeneity and Strategic Quality Decisions," Management Science, INFORMS, vol. 42(2), pages 157-172, February.
    11. Hehenkamp, Burkhard & Wambach, Achim, 2010. "Survival at the center--The stability of minimum differentiation," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 853-858, December.
    12. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    13. Edward C. Prescott & Michael Visscher, 1977. "Sequential Location among Firms with Foresight," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 378-393, Autumn.
    14. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    15. repec:ulb:ulbeco:2013/1759 is not listed on IDEAS
    16. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    17. Simon Loertscher & Gerd Muehlheusser, 2011. "Sequential location games," RAND Journal of Economics, RAND Corporation, vol. 42(4), pages 639-663, December.
    18. Berman, Oded & Gavious, Arieh, 2007. "Location of terror response facilities: A game between state and terrorist," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1113-1133, March.
    19. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    20. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    21. H. A. Eiselt & Gilbert Laporte, 1993. "The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree," Transportation Science, INFORMS, vol. 27(1), pages 39-43, February.
    22. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    23. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    24. labbe, M. & Peeters, D. & Thisse, J.F., 1992. "Location on Networks," Papers 9216, Universite Libre de Bruxelles - C.E.M.E..
    25. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753.
    26. Eiselt, H. A. & Laporte, Gilbert, 1997. "Sequential location problems," European Journal of Operational Research, Elsevier, vol. 96(2), pages 217-231, January.
    27. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    28. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    29. Gregory S. Carpenter, 1989. "Perceptual Position and Competitive Brand Strategy in a Two-Dimensional, Two-Brand Market," Management Science, INFORMS, vol. 35(9), pages 1029-1044, September.
    30. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
    31. Kieron Meagher & Klaus Zauner, 2005. "Location-then-price competition with uncertain consumer tastes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 799-818, June.
    32. Shiode, Shogo & Drezner, Zvi, 2003. "A competitive facility location problem on a tree network with stochastic weights," European Journal of Operational Research, Elsevier, vol. 149(1), pages 47-52, August.
    33. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    34. Meagher, Kieron J. & Zauner, Klaus G., 2004. "Product differentiation and location decisions under demand uncertainty," Journal of Economic Theory, Elsevier, vol. 117(2), pages 201-216, August.
    35. Martine Labbé & S. Louis Hakimi, 1991. "Market and Locational Equilibrium for Two Competitors," Operations Research, INFORMS, vol. 39(5), pages 749-756, October.
    36. de PALMA, André & HONG, Gap-Seon & THISSE, Jacques-François, 1988. "Equilibria in multi-party competition under uncertainty," LIDAM Discussion Papers CORE 1988039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    37. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
    38. Godinho, Pedro & Dias, Joana, 2010. "A two-player competitive discrete location model with simultaneous decisions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1419-1432, December.
    39. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
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    Cited by:

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    3. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    4. Dilek, Hande & Karaer, Özgen & Nadar, Emre, 2018. "Retail location competition under carbon penalty," European Journal of Operational Research, Elsevier, vol. 269(1), pages 146-158.
    5. Buechel, Berno & Klein, Jan, 2014. "Do Consumers' Preferences Really Matter? - A Note on Spatial Competition with Restricted Strategies," MPRA Paper 55288, University Library of Munich, Germany.
    6. Wen-Chung Guo & Fu-Chuan Lai, 2020. "Spatial Cournot competition in two intersecting circular markets," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(1), pages 37-56, February.

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    More about this item

    Keywords

    Location; Spatial competition; Game theory; Networks; Minimal differentiation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D49 - Microeconomics - - Market Structure, Pricing, and Design - - - Other
    • P16 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Capitalist Institutions; Welfare State
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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