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A Noncooperative Shipping Cournot Duopoly With Linear‐Quadratic Transport Costs And Circular Space

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  • TOSHIHIRO MATSUMURA
  • DAISUKE SHIMIZU

Abstract

The mixed strategy equilibria in a location quantity duopoly model with circular markets are investigated. We find that a continuum of equilibria exists when the transport cost function is linear. However, if costs are strictly concave or convex, most strategies fail to qualify as equilibria. For any integer n, there are nondegenerate mixed strategy equilibria in which each firm locates at n possible locations with equal probability. This result explains possible outcomes in which firms’ on‐path locations are not minimally or maximally differentiated.

Suggested Citation

  • Toshihiro Matsumura & Daisuke Shimizu, 2008. "A Noncooperative Shipping Cournot Duopoly With Linear‐Quadratic Transport Costs And Circular Space," The Japanese Economic Review, Japanese Economic Association, vol. 59(4), pages 498-518, December.
    • Handle: RePEc:bla:jecrev:v:59:y:2008:i:4:p:498-518
    DOI: 10.1111/j.1468-5876.2008.00428.x
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    1. Greenhut, John G & Greenhut, M L, 1975. "Spatial Price Discrimination, Competition and Locational Effects," Economica, London School of Economics and Political Science, vol. 42(168), pages 401-419, November.
    2. Hamilton, Jonathan H. & Thisse, Jacques-Francois & Weskamp, Anita, 1989. "Spatial discrimination : Bertrand vs. Cournot in a model of location choice," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 87-102, February.
    3. Wang, X. Henry & Yang, Bill Z., 2001. "Mixed-strategy equilibria in a quality differentiation model," International Journal of Industrial Organization, Elsevier, vol. 19(1-2), pages 213-226, January.
    4. P M Picard & T Tabuchi, 2003. "Natural Agglomeration," Economics Discussion Paper Series 0329, Economics, The University of Manchester.
    5. Noriaki Matsushima & Toshihiro Matsumura, 2003. "Mixed oligopoly and spatial agglomeration," Canadian Journal of Economics, Canadian Economics Association, vol. 36(1), pages 62-87, February.
    6. Toshihiro Matsumura & Takao Ohkawa & Daisuke Shimizu, 2005. "Partial Agglomeration or Dispersion in Spatial Cournot Competition," Southern Economic Journal, John Wiley & Sons, vol. 72(1), pages 224-235, July.
    7. Mayer, Thierry, 2000. "Spatial Cournot competition and heterogeneous production costs across locations," Regional Science and Urban Economics, Elsevier, vol. 30(3), pages 325-352, May.
    8. Daisuke Shimizu & Toshihiro Matsumura, 2003. "Equilibria for circular spatial Cournot markets," Economics Bulletin, AccessEcon, vol. 18(1), pages 1-9.
    9. Chamorro-Rivas, Jose-Maria, 2000. "Plant proliferation in a spatial model of Cournot competition," Regional Science and Urban Economics, Elsevier, vol. 30(5), pages 507-518, September.
    10. Bester, Helmut & de Palma, Andre & Leininger, Wolfgang & Thomas, Jonathan & von Thadden, Ernst-Ludwig, 1996. "A Noncooperative Analysis of Hotelling's Location Game," Games and Economic Behavior, Elsevier, vol. 12(2), pages 165-186, February.
    11. Matsushima, Noriaki, 2001. "Cournot competition and spatial agglomeration revisited," Economics Letters, Elsevier, vol. 73(2), pages 175-177, November.
    12. Noriaki Matsushima, 2001. "Horizontal Mergers and Merger Waves in a Location Model," Australian Economic Papers, Wiley Blackwell, vol. 40(3), pages 263-286, September.
    13. Eaton, B Curtis & Schmitt, Nicolas, 1994. "Flexible Manufacturing and Market Structure," American Economic Review, American Economic Association, vol. 84(4), pages 875-888, September.
    14. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    15. George Norman, 1981. "Spatial Competition and Spatial Price Discrimination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 97-111.
    16. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    17. Gupta, Barnali & Lai, Fu-Chuan & Pal, Debashis & Sarkar, Jyotirmoy & Yu, Chia-Ming, 2004. "Where to locate in a circular city?," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 759-782, June.
    18. Anderson, Simon P, 1988. "Equilibrium Existence in the Linear Model of Spatial Competition," Economica, London School of Economics and Political Science, vol. 55(220), pages 479-491, November.
    19. Toshihiro Matsumura, 2004. "Strategic Complementarity in Direct Investments," Review of Development Economics, Wiley Blackwell, vol. 8(4), pages 583-596, November.
    20. Toshihiro Matsumura & Noriaki Matsushima, 2005. "Cartel Stability in a Delivered Pricing Oligopoly," Journal of Economics, Springer, vol. 86(3), pages 259-292, December.
    21. Barnali Gupta, 2004. "Spatial Cournot competition in a circular city with transport cost differentials," Economics Bulletin, AccessEcon, vol. 4(15), pages 1-6.
    22. Barnali Gupta & Guhan Venkatu, 2002. "Tacit Collusion in a Spatial Model with Delivered Pricing," Journal of Economics, Springer, vol. 76(1), pages 49-64, May.
    23. Pal, Debashis, 1998. "Does Cournot competition yield spatial agglomeration?," Economics Letters, Elsevier, vol. 60(1), pages 49-53, July.
    24. Toshihiro Matsumura, 2003. "Consumer‐benefiting exclusive territories," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 1007-1025, November.
    25. Jonathan H Hamilton & James F. Klein & Eytan Sheshinski & Steven M. Slutsky, 1994. "Quantity Competition in a Spatial Model," Canadian Journal of Economics, Canadian Economics Association, vol. 27(4), pages 903-917, November.
    26. Shimizu, Daisuke, 2002. "Product differentiation in spatial Cournot markets," Economics Letters, Elsevier, vol. 76(3), pages 317-322, August.
    27. Anderson, Simon P & Neven, Damien J, 1991. "Cournot Competition Yields Spatial Agglomeration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(4), pages 793-808, November.
    28. Matsumura, Toshihiro & Shimizu, Daisuke, 2005. "Spatial Cournot competition and economic welfare: a note," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 658-670, November.
    29. Simon P. Anderson & André De Palma, 1988. "Spatial Price Discrimination with Heterogeneous Products," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 573-592.
    30. Norman, George & Thisse, Jacques-Francois, 1999. "Technology Choice and Market Structure: Strategic Aspects of Flexible Manufacturing," Journal of Industrial Economics, Wiley Blackwell, vol. 47(3), pages 345-372, September.
    31. repec:ebl:ecbull:v:4:y:2004:i:15:p:1-6 is not listed on IDEAS
    32. repec:ebl:ecbull:v:18:y:2003:i:1:p:1-9 is not listed on IDEAS
    33. Matsumura, Toshihiro & Okamura, Makoto, 2006. "Equilibrium number of firms and economic welfare in a spatial price discrimination model," Economics Letters, Elsevier, vol. 90(3), pages 396-401, March.
    34. Matsushima, Noriaki, 2001. "Horizontal Mergers and Merger Waves in a Location Model," Australian Economic Papers, Wiley Blackwell, vol. 40(3), pages 263-286, September.
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    Cited by:

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    2. Chia-Hung Sun & Jyh-Fa Tsai & Fu-Chuan Lai, 2017. "Spatial Cournot competition in a circular city with more than two dispatches," The Japanese Economic Review, Japanese Economic Association, vol. 68(4), pages 413-442, December.
    3. Toshihiro Matsumura & Noriaki Matsushima, 2012. "Spatial Cournot competition and transportation costs in a circular city," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(1), pages 33-44, February.
    4. Toshihiro Matsumura & Daisuke Shimizu, 2015. "Endogenous Flexibility In The Flexible Manufacturing System," Bulletin of Economic Research, Wiley Blackwell, vol. 67(1), pages 1-13, January.
    5. Stefano Colombo, 2016. "A Model of Three Cities," International Regional Science Review, , vol. 39(4), pages 386-416, October.

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