IDEAS home Printed from https://ideas.repec.org/p/jau/wpaper/2013-04.html
   My bibliography  Save this paper

Stagnation proofness and individually monotonic bargaining solutions

Author

Listed:
  • Jaume García-Segarra

    (LEE & Department of Economics, Universitat Jaume I, Castellón, Spain)

  • Miguel Ginés-Vilar

    (LEE & Department of Economics, Universitat Jaume I, Castellón, Spain)

Abstract

The aim of this paper is to generalize the results of Peter and Tijs [10] and [9]. We propose a characterization that holds both for n-agent problems and for a larger class of problems. The axioms used in our characterization are weaker because they are implied by the characterization in the aforementioned references. We analyze a phenomenon known as stagnation effect, which takes place when a bargaining solution remains unchanged facing all possible expansions of the bargaining set not affecting the utopia point. Our main result relies on a very weak axiom, stagnation proofness. Whenever a bargaining solution satisfies this axiom, such solution does not suffer from the stagnation effect.

Suggested Citation

  • Jaume García-Segarra & Miguel Ginés-Vilar, 2013. "Stagnation proofness and individually monotonic bargaining solutions," Working Papers 2013/04, Economics Department, Universitat Jaume I, Castellón (Spain).
    • Handle: RePEc:jau:wpaper:2013/04
    as

    Download full text from publisher

    File URL: http://www.doctreballeco.uji.es/wpficheros/Garcia_Gines_04_2013.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    3. Robert W. Rosenthal, 1976. "An Arbitration Model for Normal-Form Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 82-88, February.
    4. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    5. Peters, H.J.M. & Tijs, S.H., 1984. "Individually monotonic bargaining solutions of n-person bargaining games," Other publications TiSEM 94ffcb19-a0bc-4364-a42e-7, Tilburg University, School of Economics and Management.
    6. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    8. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
    9. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    10. Driesen, Bram W., 2012. "The Asymmetric Leximin Solution," Working Papers 0523, University of Heidelberg, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    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. Jaume García-Segarra & Miguel Ginés-Vilar, 2019. "Stagnation proofness in n-agent bargaining problems," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 215-224, March.
    2. Jaume García Segarra & Miguel Ginés Vilar, 2011. "Weighted Proportional Losses Solution," ThE Papers 10/21, Department of Economic Theory and Economic History of the University of Granada..
    3. Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    4. Jaume Garcia-Segarra & Miguel Gines-Vilar, 2012. "The stagnation effect and the individually strict monotonic path solutions," Working Papers 2012/10, Economics Department, Universitat Jaume I, Castellón (Spain).
    5. Dominik Karos & Nozomu Muto & Shiran Rachmilevitch, 2018. "A generalization of the Egalitarian and the Kalai–Smorodinsky bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1169-1182, November.
    6. Naeve-Steinweg, Elisabeth, 2002. "Mechanisms supporting the Kalai-Smorodinsky solution," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 25-36, September.
    7. l'Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2013. "Does bargaining matter in the small firms matching model?," Labour Economics, Elsevier, vol. 21(C), pages 42-58.
    8. Forgo, F. & Szidarovszky, F., 2003. "On the relation between the Nash bargaining solution and the weighting method," European Journal of Operational Research, Elsevier, vol. 147(1), pages 108-116, May.
    9. Claus-Jochen Haake & Cheng-Zhong Qin, 2018. "On unification of solutions to the bargaining problem," Working Papers CIE 113, Paderborn University, CIE Center for International Economics.
    10. Younghwan In, 2008. "On the relevance of alternatives in bargaining: generalized average pay-off solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 251-264, June.
    11. Youngsub Chun, 2021. "Axioms concerning uncertain disagreement points in 2-person bargaining problems," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 6(1), pages 37-58, December.
    12. Youngsub Chun, 2020. "Some Impossibility Results on the Converse Consistency Principle in Bargaining," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 59-65, November.
    13. Driesen, Bram W., 2012. "The Asymmetric Leximin Solution," Working Papers 0523, University of Heidelberg, Department of Economics.
    14. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    15. Gerber, Anke & Upmann, Thorsten, 2006. "Bargaining solutions at work: Qualitative differences in policy implications," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 162-175, September.
    16. 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.
    17. Bram Driesen, 2016. "Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 777-809, April.
    18. Rachmilevitch, Shiran, "undated". "Gradual Negotiations and Proportional Solutions," Working Papers WP2011/8, University of Haifa, Department of Economics.
    19. José-Manuel Giménez-Gómez & António Osório & Josep E. Peris, 2015. "From Bargaining Solutions to Claims Rules: A Proportional Approach," Games, MDPI, vol. 6(1), pages 1-7, March.
    20. Kristal K. Trejo & Julio B. Clempner & Alexander S. Poznyak, 2019. "Computing the Bargaining Approach for Equalizing the Ratios of Maximal Gains in Continuous-Time Markov Chains Games," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 933-955, October.

    More about this item

    Keywords

    Bargaining; axiomatization; n-agent problem; monotone paths;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    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:jau:wpaper:2013/04. 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: María Aurora Garcia Gallego (email available below). General contact details of provider: https://edirc.repec.org/data/ueujies.html .

    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.