IDEAS home Printed from https://ideas.repec.org/p/ajk/ajkdps/005.html
   My bibliography  Save this paper

A General Framework for Studying Contests

Author

Listed:
  • Spencer Bastani

    (Department of Economics and Statistics, School of Business and Economics, Linnaeus University,Sweden)

  • Thomas Giebe

    (Department of Economics and Statistics, School of Business and Economics, Linnaeus University,Sweden)

  • Oliver Gürtler

    (Department of Economics, University of Cologne, Germany)

Abstract

We develop a general framework for studying contests, including the well-known models of Tullock(1980) and Lazear & Rosen (1981) as special cases. The contest outcome depends on players’ efforts and skills, the latter being subject to symmetric uncertainty. The model is tractable, because asymmetric equilibrium exists under general assumptions regarding production technologies and skill distributions. Using a link between our contest model and expected utility theory, we are able to derive new comparative statics results regarding how the size and composition of contests affect equilibrium effort, showing how standard results can be overturned. We also discuss the robustness ofour results to changes in the information structure and the implications of our findings for the optimal design of teams.

Suggested Citation

  • Spencer Bastani & Thomas Giebe & Oliver Gürtler, 2020. "A General Framework for Studying Contests," ECONtribute Discussion Papers Series 005, University of Bonn and University of Cologne, Germany.
    • Handle: RePEc:ajk:ajkdps:005
    as

    Download full text from publisher

    File URL: https://www.econtribute.de/RePEc/ajk/ajkdps/ECONtribute_005_2020.pdf
    File Function: First version, 2020
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Giebe, Thomas & Schweinzer, Paul, 2014. "Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries," European Journal of Political Economy, Elsevier, vol. 36(C), pages 1-12.
    2. Scott M Gilpatric, 2009. "Risk Taking In Contests And The Role Of Carrots And Sticks," Economic Inquiry, Western Economic Association International, vol. 47(2), pages 266-277, April.
    3. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    4. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    5. David Bjerk, 2008. "Glass Ceilings or Sticky Floors? Statistical Discrimination in a Dynamic Model of Hiring and Promotion," Economic Journal, Royal Economic Society, vol. 118(530), pages 961-982, July.
    6. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    7. Heski Bar-Isaac & Raphaël Lévy, 2022. "Motivating Employees through Career Paths," Journal of Labor Economics, University of Chicago Press, vol. 40(1), pages 95-131.
    8. Jennifer Brown, 2011. "Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars," Journal of Political Economy, University of Chicago Press, vol. 119(5), pages 982-1013.
    9. Thomas Giebe & Paul Schweinzer, 2012. "Fuzzy Price-Quality Ratio Procurement under Incomplete Information," Discussion Papers 12/26, Department of Economics, University of York.
    10. Chowdhury, Subhasish M. & Kim, Sang-Hyun, 2017. "“Small, yet Beautiful”: Reconsidering the optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 104(C), pages 486-493.
    11. Kräkel, Matthias, 2008. "Optimal risk taking in an uneven tournament game with risk averse players," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1219-1231, December.
    12. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    13. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    14. Dan Bernhardt, 1995. "Strategic Promotion and Compensation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 315-339.
    15. Qiang Fu & Jingfeng Lu, 2012. "Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 497-517, March.
    16. Christian Grund & Dirk Sliwka, 2005. "Envy and Compassion in Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(1), pages 187-207, March.
    17. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    18. Jed DeVaro & Antti Kauhanen, 2016. "An “Opposing Responses” Test of Classic versus Market-Based Promotion Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 34(3), pages 747-779.
    19. Alex Krumer & Reut Megidish & Aner Sela, 2017. "Round‐Robin Tournaments with a Dominant Player," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(4), pages 1167-1200, October.
    20. Andrew Schotter & Keith Weigelt, 1992. "Asymmetric Tournaments, Equal Opportunity Laws, and Affirmative Action: Some Experimental Results," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 511-539.
    21. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    22. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).
    23. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    24. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    25. Lazear, Edward P, 1989. "Pay Equality and Industrial Politics," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 561-580, June.
    26. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    27. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    28. James M. Malcomson, 1986. "Rank-Order Contracts for a Principal with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 807-817.
    29. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    30. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451, June.
    31. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 99-129, September.
    32. Matthias Kräkel & Dirk Sliwka, 2004. "Risk Taking in Asymmetric Tournaments," German Economic Review, Verein für Socialpolitik, vol. 5(1), pages 103-116, February.
    33. Qiang Fu & Jingfeng Lu & Yue Pan, 2015. "Team Contests with Multiple Pairwise Battles," American Economic Review, American Economic Association, vol. 105(7), pages 2120-2140, July.
    34. Gürtler, Oliver & Kräkel, Matthias, 2010. "Optimal tournament contracts for heterogeneous workers," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 180-191, August.
    35. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    36. Gershkov, Alex & Li, Jianpei & Schweinzer, Paul, 2016. "How to share it out: The value of information in teams," Journal of Economic Theory, Elsevier, vol. 162(C), pages 261-304.
    37. Subhasish Chowdhury & Oliver Gürtler, 2015. "Sabotage in contests: a survey," Public Choice, Springer, vol. 164(1), pages 135-155, July.
    38. Hideo Owan, 2004. "Promotion, Turnover, Earnings, and Firm-Sponsored Training," Journal of Labor Economics, University of Chicago Press, vol. 22(4), pages 955-978, October.
    39. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    40. Jed DeVaro & Michael Waldman, 2012. "The Signaling Role of Promotions: Further Theory and Empirical Evidence," Journal of Labor Economics, University of Chicago Press, vol. 30(1), pages 91-147.
    41. Marc Gürtler & Oliver Gürtler, 2015. "The Optimality of Heterogeneous Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 33(4), pages 1007-1042.
    42. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    43. Kong-Pin Chen, 2003. "Sabotage in Promotion Tournaments," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 19(1), pages 119-140, April.
    44. Oliver Gürtler & Johannes Münster & Petra Nieken, 2013. "Information Policy in Tournaments with Sabotage," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(3), pages 932-966, July.
    45. Lorens Imhof & Matthias Kräkel, 2016. "Ex post unbalanced tournaments," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 73-98, February.
    46. Alex Gershkov & Jianpei Li & Paul Schweinzer, 2009. "Efficient tournaments within teams," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 103-119, March.
    47. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 881-914, August.
    48. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    49. Anja Schöttner & Veikko Thiele, 2010. "Promotion Tournaments and Individual Performance Pay," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 699-731, September.
    50. Suman Ghosh & Michael Waldman, 2010. "Standard promotion practices versus up‐or‐out contracts," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 301-325, June.
    51. David Bjerk, 2008. "Glass Ceilings or Sticky Floors? Statistical Discrimination in a Dynamic Model of Hiring and Promotion," Economic Journal, Royal Economic Society, vol. 118(530), pages 961-982, July.
    52. Stefano Barbieri & David Malueg & Iryna Topolyan, 2014. "The best-shot all-pay (group) auction with complete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 603-640, November.
    53. Michael Waldman, 1984. "Job Assignments, Signalling, and Efficiency," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 255-267, Summer.
    54. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    55. Yigal Gerchak & Qi-Ming He, 2003. "When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 151-165.
    56. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    57. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    58. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-289, March.
    59. Florian Ederer, 2010. "Feedback and Motivation in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 733-769, September.
    60. Mathias Dewatripont & Ian Jewitt & Jean Tirole, 1999. "The Economics of Career Concerns, Part I: Comparing Information Structures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 183-198.
    61. Luis Corchón & Matthias Dahm, 2010. "Foundations for contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 81-98, April.
    62. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    63. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    64. Dawei Fang & Thomas Noe & Philipp Strack, 2020. "Turning Up the Heat: The Discouraging Effect of Competition in Contests," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1940-1975.
    65. Emmanuelle Auriol & Guido Friebel & Lambros Pechlivanos, 2002. "Career Concerns in Teams," Journal of Labor Economics, University of Chicago Press, vol. 20(2), pages 289-307, Part.
    66. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    67. Fu, Qiang & Wu, Zenan, 2020. "On the optimal design of biased contests," Theoretical Economics, Econometric Society, vol. 15(4), November.
    68. Mathias Dewatripont & Ian Jewitt & Jean Tirole, 1999. "The Economics of Career Concerns, Part I: Comparing Information Structures," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 183-198.
    69. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 881-914, August.
    70. Thomas Giebe & Paul Schweinzer, 2015. "Probabilistic procurement auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 19(1), pages 25-46, March.
    71. Malcomson, James M, 1984. "Work Incentives, Hierarchy, and Internal Labor Markets," Journal of Political Economy, University of Chicago Press, vol. 92(3), pages 486-507, June.
    72. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    73. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    74. Aoyagi, Masaki, 2010. "Information feedback in a dynamic tournament," Games and Economic Behavior, Elsevier, vol. 70(2), pages 242-260, November.
    75. Clark, D.J. & Riis, C., 1996. "On the Win Probability in Rent-Seeking Gemes," Memorandum 1996_005, Oslo University, Department of Economics.
    76. Fu, Qiang & Lu, Jingfeng, 2009. "The beauty of "bigness": On optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 146-161, May.
    77. Jan Zábojník & Dan Bernhardt, 2001. "Corporate Tournaments, Human Capital Acquisition, and the Firm Size—Wage Relation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 693-716.
    78. O'Keeffe, Mary & Viscusi, W Kip & Zeckhauser, Richard J, 1984. "Economic Contests: Comparative Reward Schemes," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 27-56, January.
    79. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    2. Merve İntişah & Mürüvvet Büyükboyacı, 2024. "The role of noise variance on effort in group contests," Theory and Decision, Springer, vol. 97(2), pages 311-346, September.
    3. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).
    4. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    5. Hanming Fang & Ming Li & Zenan Wu, 2022. "Tournament-Style Political Competition and Local Protectionism: Theory and Evidence from China," NBER Working Papers 30780, National Bureau of Economic Research, Inc.
    6. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    7. Giebe, Thomas & Gürtler, Oliver, 2024. "Player strength and effort in contests," Working Papers in Economics and Statistics 4/2024, Linnaeus University, School of Business and Economics, Department of Economics and Statistics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    2. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    3. Cedric Duvinage & Peter-J. Jost, 2019. "The Role of Referees in Professional Sports Contests," Journal of Sports Economics, , vol. 20(8), pages 1014-1050, December.
    4. Dahm, Matthias & Esteve-González, Patricia, 2018. "Affirmative action through extra prizes," Journal of Economic Behavior & Organization, Elsevier, vol. 153(C), pages 123-142.
    5. Cason, Timothy N. & Masters, William A. & Sheremeta, Roman M., 2020. "Winner-take-all and proportional-prize contests: Theory and experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 314-327.
    6. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    7. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    8. Loukas Balafoutas & E. Glenn Dutcher & Florian Lindner & Dmitry Ryvkin, 2017. "The Optimal Allocation Of Prizes In Tournaments Of Heterogeneous Agents," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 461-478, January.
    9. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    11. Kräkel, Matthias & Schöttner, Anja, 2010. "Technology choice, relative performance pay, and worker heterogeneity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 748-758, December.
    12. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    13. Ján Zábojník, 2012. "Promotion tournaments in market equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 213-240, September.
    14. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    15. Fu, Qiang & Wang, Xiruo & Wu, Zenan, 2021. "Multi-prize contests with risk-averse players," Games and Economic Behavior, Elsevier, vol. 129(C), pages 513-535.
    16. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    17. Waldman, Michael, 2013. "Classic promotion tournaments versus market-based tournaments," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 198-210.
    18. Jed DeVaro & Antti Kauhanen, 2016. "An “Opposing Responses” Test of Classic versus Market-Based Promotion Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 34(3), pages 747-779.
    19. Barbieri, Stefano & Serena, Marco, 2022. "Biasing dynamic contests between ex-ante symmetric players," Games and Economic Behavior, Elsevier, vol. 136(C), pages 1-30.
    20. Jed DeVaro & Suman Ghosh & Cindy Zoghi, 2018. "Job Characteristics and Labor Market Discrimination in Promotions," Industrial Relations: A Journal of Economy and Society, Wiley Blackwell, vol. 57(3), pages 389-434, July.

    More about this item

    Keywords

    contest theory; symmetric equilibrium; heterogeneity; risk; stochastic dominance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • J23 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Demand
    • M51 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Firm Employment Decisions; Promotions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ajk:ajkdps:005. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ECONtribute Office (email available below). General contact details of provider: https://www.econtribute.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.