IDEAS home Printed from https://ideas.repec.org/p/aub/autbar/678.07.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this paper

Payoff-dependent balancedness and cores (revised version)

Author

Abstract

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

Suggested Citation

  • Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:678.07
    as

    Download full text from publisher

    File URL: http://pareto.uab.es/wp/2007/67807.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
    2. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    3. Kannai, Yakar & Wooders, Myrna H., 1999. "A Further Extension of the KKMS Theorem," Economic Research Papers 269259, University of Warwick - Department of Economics.
    4. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    5. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
    6. P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
    7. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    8. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    9. Ichiishi, Tatsuro & Quinzii, Martine, 1983. "Decentralization for the Core of a Production Economy with Increasing Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 397-412, June.
    10. Bonnisseau, J.M., 1995. "Existence of Equilibria in Economies with Externalities and Non Convexities," Papiers d'Economie Mathématique et Applications 95.45, Université Panthéon-Sorbonne (Paris 1).
    11. Vohra, Rajiv, 1988. "On the existence of equilibria in economies with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 179-192, April.
    12. Ichiishi, Tatsuro & Idzik, Adam, 1996. "Bayesian Cooperative Choice of Strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(4), pages 455-473.
    13. repec:dau:papers:123456789/5454 is not listed on IDEAS
    14. Vincent Iehlé, 2004. "Transfer rate rules and core selections in NTU games," Economics Bulletin, AccessEcon, vol. 3(42), pages 1-10.
    15. 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.
    16. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    17. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    18. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
    19. Adam Idzik & Tatsuro Ichiishi, 2002. "On a covering theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 833-838.
    20. Roy Radner & Tatsuro Ichiishi, 1999. "A profit-center game with incomplete information," Review of Economic Design, Springer;Society for Economic Design, vol. 4(4), pages 307-343.
    21. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
    22. Francoise Forges & Jean-Francois Mertens & Rajiv Vohra, 2002. "The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects," Econometrica, Econometric Society, vol. 70(5), pages 1865-1892, September.
    23. Kajii, Atsushi, 1992. "A generalization of Scarf's theorem: An [alpha]-core existence theorem without transitivity or completeness," Journal of Economic Theory, Elsevier, vol. 56(1), pages 194-205, February.
    24. Yakar Kannai & Myrna H. Wooders, 2000. "A Further Extension of the KKMS Theorem," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 539-551, November.
    25. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    26. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    27. Reny, Philip J. & Holtz Wooders, Myrna, 1998. "An extension of the KKMS theorem," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 125-134, March.
    28. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    29. Orshan, Gooni & Zarzuelo, Jose M., 2000. "The Bilateral Consistent Prekernel for NTU Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 67-84, July.
    30. Volker Boehm, 1974. "The Core of an Economy with Production," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(3), pages 429-436.
    31. Greenberg, Joseph, 1994. "Coalition structures," 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 37, pages 1305-1337, Elsevier.
    32. Ichiishi,Tatsuro, 1993. "The Cooperative Nature of the Firm," Cambridge Books, Cambridge University Press, number 9780521414449, November.
    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. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    2. Yan-An Hwang & Yu-Hsien Liao, 2022. "The Replicated Core under Multi-Choice Non-Transferable- Utility Situations: Converse Reduction Axiomatic Enlargements," Mathematics, MDPI, vol. 10(5), pages 1-8, March.
    3. Sonja Brangewitz & Jan-Philip Gamp, 2014. "Competitive outcomes and the inner core of NTU market games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 529-554, November.
    4. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    5. Yan-An Hwang & Yu-Hsien Liao, 2020. "A Solution Concept and Its Axiomatic Results under Non-Transferable-Utility and Multi-Choice Situations," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    6. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    7. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.
    8. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.

    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. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    2. repec:dau:papers:123456789/89 is not listed on IDEAS
    3. Yang, Zhe & Zhang, Xian, 2021. "A weak α-core existence theorem of games with nonordered preferences and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    4. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    5. Philip Reny & Eyal Winter & Myrna Wooders, 2012. "The partnered core of a game with side payments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 521-536, July.
    6. Yakar Kannai & Wooders, Myrna H., 1999. "A Further Extension of the KKMS Theorem," The Warwick Economics Research Paper Series (TWERPS) 538, University of Warwick, Department of Economics.
    7. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    8. 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.
    9. Vincent Iehlé, 2004. "Transfer rate rules and core selections in NTU games," Economics Bulletin, AccessEcon, vol. 3(42), pages 1-10.
    10. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    11. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    12. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.
    13. Dutta, Bhaskar & Vohra, Rajiv, 2005. "Incomplete information, credibility and the core," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 148-165, September.
    14. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    15. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Reny, Philip J. & Holtz Wooders, Myrna, 1998. "An extension of the KKMS theorem," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 125-134, March.
    17. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    18. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
    19. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    20. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    21. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.

    More about this item

    Keywords

    balancedness; cooperative game; core; parametrized game;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    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:aub:autbar:678.07. 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: Xavier Vila (email available below). General contact details of provider: https://edirc.repec.org/data/ufuabes.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.