IDEAS home Printed from https://ideas.repec.org/a/spr/series/v12y2021i1d10.1007_s13209-020-00221-5.html
   My bibliography  Save this article

Sixty-seven years of the Nash program: time for retirement?

Author

Listed:
  • Roberto Serrano

    (Brown University)

Abstract

The Nash program is an important research agenda initiated in Nash (Econometrica 21:128–140, 1953) in order to bridge the gap between the noncooperative and cooperative counterparts of game theory. The program is thus turning sixty-seven years old, but I will argue it is not ready for retirement, as it is full of energy and one can still propose important directions to be explored. This paper completes and updates previous surveys, and suggests several directions for future research.

Suggested Citation

  • Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
  • Handle: RePEc:spr:series:v:12:y:2021:i:1:d:10.1007_s13209-020-00221-5
    DOI: 10.1007/s13209-020-00221-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13209-020-00221-5
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1007/s13209-020-00221-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Haake, Claus-Jochen, 2009. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 177-187, March.
    2. Marco Rogna, 2022. "The Burning Coalition Bargaining Model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 735-768, October.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Ricardo Nieva, 2015. "The Coalitional Nash Bargaining Solution with Simultaneous Payoff Demands," Working Papers 2015.67, Fondazione Eni Enrico Mattei.
    5. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
    6. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    7. Burguet, Roberto & Caminal, Ramon, 2020. "Coalitional bargaining with consistent counterfactuals," Journal of Economic Theory, Elsevier, vol. 187(C).
    8. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
    9. Chander, Parkash & Wooders, Myrna, 2020. "Subgame-perfect cooperation in an extensive game," Journal of Economic Theory, Elsevier, vol. 187(C).
    10. de Clippel, Geoffroy, 2007. "The type-agent core for exchange economies with asymmetric information," Journal of Economic Theory, Elsevier, vol. 135(1), pages 144-158, July.
    11. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2006. "Efficient bidding with externalities," Games and Economic Behavior, Elsevier, vol. 57(2), pages 304-320, November.
    12. Serrano, Roberto & Vohra, Rajiv, 2007. "Information transmission in coalitional voting games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 117-137, May.
    13. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    14. John F. Nash, 2008. "The Agencies Method For Modeling Coalitions And Cooperation In Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 539-564.
    15. Y. H. Gu & M. Goh & Q. L. Chen & R. D. Souza & G. C. Tang, 2013. "A new two-party bargaining mechanism," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 135-163, January.
    16. Guth, Werner & Ritzberger, Klaus & van Damme, Eric, 2004. "On the Nash bargaining solution with noise," European Economic Review, Elsevier, vol. 48(3), pages 697-713, June.
    17. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2014. "On the convergence to the Nash bargaining solution for action-dependent bargaining protocols," Games and Economic Behavior, Elsevier, vol. 86(C), pages 178-183.
    18. McQuillin, Ben, 2009. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," Journal of Economic Theory, Elsevier, vol. 144(2), pages 696-721, March.
    19. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    20. Françoise Forges & Roberto Serrano, 2013. "Cooperative Games With Incomplete Information: Some Open Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-17.
    21. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    22. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    23. In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
    24. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    25. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
    26. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
    27. Johannes Spinnewijn & Frans Spinnewyn, 2015. "Revising claims and resisting ultimatums in bargaining problems," Review of Economic Design, Springer;Society for Economic Design, vol. 19(2), pages 91-116, June.
    28. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    29. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, vol. 78(5), pages 1593-1623, September.
    30. Van Essen, Matthew, 2014. "A Simple Bargaining Model where Parties Make Errors," MPRA Paper 58952, University Library of Munich, Germany.
    31. Anbarci, Nejat & Sun, Ching-jen, 2013. "Asymmetric Nash bargaining solutions: A simple Nash program," Economics Letters, Elsevier, vol. 120(2), pages 211-214.
    32. Kamijo, Yoshio, 2008. "Implementation of weighted values in hierarchical and horizontal cooperation structures," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 336-349, November.
    33. Borm, Peter & Ju, Yuan & Wettstein, David, 2015. "Rational bargaining in games with coalitional externalities," Journal of Economic Theory, Elsevier, vol. 157(C), pages 236-254.
    34. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    35. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
    36. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    37. Ben McQuillin & Robert Sugden, 2016. "Backward Induction Foundations of the Shapley Value," Econometrica, Econometric Society, vol. 84, pages 2265-2280, November.
    38. Adam Kalai & Ehud Kalai, 2013. "Cooperation in Strategic Games Revisited," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 917-966.
    39. Frã‰Chette, Guillaume R. & Kagel, John H. & Lehrer, Steven F., 2003. "Bargaining in Legislatures: An Experimental Investigation of Open versus Closed Amendment Rules," American Political Science Review, Cambridge University Press, vol. 97(2), pages 221-232, May.
    40. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    41. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    42. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    43. Nejat Anbarci, 2006. "Finite Alternating-Move Arbitration Schemes and the Equal Area Solution," Theory and Decision, Springer, vol. 61(1), pages 21-50, August.
    44. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    45. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.
    46. Dilip Abreu & David Pearce, 2015. "A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats," Econometrica, Econometric Society, vol. 83(4), pages 1641-1655, July.
    47. Okada, Akira, 2010. "The Nash bargaining solution in general n-person cooperative games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2356-2379, November.
    48. Michela Chessa, 2019. "A Shapley-based Groves mechanism: when the mechanism designer plays the wise man," Post-Print hal-02390679, HAL.
    49. Guillaume Fréchette & John H. Kagel & Massimo Morelli, 2005. "Behavioral Identification in Coalitional Bargaining: An Experimental Analysis of Demand Bargaining and Alternating Offers," Econometrica, Econometric Society, vol. 73(6), pages 1893-1937, November.
    50. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    51. Forges, Francoise & Minelli, Enrico & Vohra, Rajiv, 2002. "Incentives and the core of an exchange economy: a survey," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 1-41, September.
    52. Qin, Cheng-Zhong & Tan, Guofu & Wong, Adam Chi Leung, 2019. "Implementation of Nash bargaining solutions with non-convexity," Economics Letters, Elsevier, vol. 178(C), pages 46-49.
    53. Mizukami, Hideki & Wakayama, Takuma, 2020. "Dominant strategy implementation of bargaining solutions," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 60-67.
    54. Tsay, Min-Hung & Yeh, Chun-Hsien, 2019. "Relations among the central rules in bankruptcy problems: A strategic perspective," Games and Economic Behavior, Elsevier, vol. 113(C), pages 515-532.
    55. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
    56. Vidal-Puga, Juan, 2015. "A non-cooperative approach to the ordinal Shapley–Shubik rule," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 111-118.
    57. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.
    58. Kawamori, Tomohiko, 2014. "A noncooperative foundation of the asymmetric Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 12-15.
    59. repec:dau:papers:123456789/8158 is not listed on IDEAS
    60. Yuan Ju, 2013. "Efficiency and compromise: a bid-offer–counteroffer mechanism with two players," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 501-520, May.
    61. Anbarci, Nejat & Feltovich, Nick, 2012. "Bargaining with random implementation: An experimental study," Games and Economic Behavior, Elsevier, vol. 76(2), pages 495-514.
    62. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    63. Hu, Tai-Wei & Rocheteau, Guillaume, 2020. "Bargaining under liquidity constraints: Unified strategic foundations of the Nash and Kalai solutions," Journal of Economic Theory, Elsevier, vol. 189(C).
    64. Serrano, Roberto & Shimomura, Ken-Ichi, 2006. "A comparison of the average prekernel and the prekernel," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 288-301, December.
    65. Rong Kang, 2012. "An Axiomatic Approach to Arbitration and its Application in Bargaining Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-34, September.
    66. Chih Chang & Cheng-Cheng Hu, 2017. "A non-cooperative interpretation of the kernel," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 185-204, March.
    67. Bram Driesen & Peter Eccles & Nora Wegner, 2017. "A non-cooperative foundation for the continuous Raiffa solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1115-1135, November.
    68. Partha Dasgupta & Eric S. Maskin, 2007. "Bargaining and Destructive Power," Annals of Economics and Finance, Society for AEF, vol. 8(2), pages 217-227, November.
    69. Miyakawa, Toshiji, 2008. "Note on the equal split solution in an n-person noncooperative bargaining game," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 281-291, May.
    70. Roberto Serrano, 2014. "The Nash Program: a broader interpretation," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 105-106, November.
    71. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
    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. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    2. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    3. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2022. "The effect of choosing a proposer through a bidding procedure in implementing the Shapley value," Journal of Economic Psychology, Elsevier, vol. 93(C).
    4. Sun, Chaoran, 2022. "Bidding against a Buyout: Implementing the Shapley value and the equal surplus value," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    5. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    6. Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2023. "An Experiment on Demand Commitment Bargaining," Dynamic Games and Applications, Springer, vol. 13(2), pages 589-609, June.
    7. Akira Okada, 2023. "Dynamic bargaining with voluntary participation and externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 427-452, February.
    8. Bouwhuis, Dirck & Borm, Peter & Hendrickx, Ruud, 2023. "A Strategic Approach to Bankruptcy Problems Based on the TAL Family of Rules," Other publications TiSEM 250808dd-6109-4708-b175-d, Tilburg University, School of Economics and Management.
    9. Matt Van Essen & John Wooders, 2023. "Dual auctions for assigning winners and compensating losers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1069-1114, November.
    10. Demeze-Jouatsa, Ghislain-Herman & Pongou, Roland & Tondji, Jean-Baptiste, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Center for Mathematical Economics Working Papers 653, Center for Mathematical Economics, Bielefeld University.
    11. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    12. Bouwhuis, Dirck & Borm, Peter & Hendrickx, Ruud, 2023. "A Strategic Approach to Bankruptcy Problems Based on the TAL Family of Rules," Discussion Paper 2023-020, Tilburg University, Center for Economic Research.
    13. Dmitry Levando, 2021. "Formation of coalition structures as a non-cooperative game," Papers 2107.00711, arXiv.org.

    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. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    2. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    3. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    4. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    5. Andrea Caggese & Ander Pérez-Orive, 2017. "Capital Misallocation and Secular Stagnation," Finance and Economics Discussion Series 2017-009, Board of Governors of the Federal Reserve System (U.S.).
    6. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2017. "Extensions of the Shapley value for Environments with Externalities," Working Papers 1002, Barcelona School of Economics.
    7. Sun, Chaoran, 2022. "Bidding against a Buyout: Implementing the Shapley value and the equal surplus value," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    8. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, July.
    9. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    10. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    11. Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2021. "An Experiment on the Nash Program: Comparing two Mechanisms Implementing the Shapley Value," GREDEG Working Papers 2021-07, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    12. Juan D. Moreno‐Ternero & Min‐Hung Tsay & Chun‐Hsien Yeh, 2022. "Strategic justifications of the TAL family of rules for bankruptcy problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 92-102, March.
    13. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
    14. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.
    15. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    16. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    17. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.
    18. Marco Rogna, 2022. "The Burning Coalition Bargaining Model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 735-768, October.
    19. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
    20. Pérez-Castrillo, David & Quérou, Nicolas, 2012. "Smooth multibidding mechanisms," Games and Economic Behavior, Elsevier, vol. 76(2), pages 420-438.

    More about this item

    Keywords

    Nash program; Bargaining; Implementation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:spr:series:v:12:y:2021:i:1:d:10.1007_s13209-020-00221-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.