IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/601.html
   My bibliography  Save this paper

Cominimum Additive Operators

Author

Listed:
  • Atsushi Kajii

    (Institute of Economic Research, Kyoto University)

  • Hiroyuki Kojima

    (Department of Economics, Teikyo University)

  • Takashi Ui

    (Faculty of Economics, Yokohama National University)

Abstract

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space \omega, which include additivity and comonotonic additivity as extreme cases. Let \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are \epsilon-cominimum if, for each E \subseteq \epsilon, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on is E- cominimum additive if I(x+y) = I(x)+I(y) whenever x and y are \epsilon-cominimum. The main result characterizes homogeneous E-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey (1999) and that of the multi-period decision model of Gilboa (1989).

Suggested Citation

  • Atsushi Kajii & Hiroyuki Kojima & Takashi Ui, 2005. "Cominimum Additive Operators," KIER Working Papers 601, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:601
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP601.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    2. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, 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. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    2. Takao Asano & Hiroyuki Kojima, 2014. "Modularity and monotonicity of games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 29-46, August.
    3. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
    4. Daniel Li Li & Erfang Shan, 2020. "Marginal contributions and derivatives for set functions in cooperative games," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 849-858, April.
    5. Takashi Ui & Hiroyuki Kojima & Atsushi Kajii, 2011. "The Myerson value for complete coalition structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 427-443, December.
    6. Takao Asano & Hiroyuki Kojima, 2015. "An axiomatization of Choquet expected utility with cominimum independence," Theory and Decision, Springer, vol. 78(1), pages 117-139, January.

    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. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    2. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    3. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2017. "Optimal sharing with an infinite number of commodities in the presence of optimistic and pessimistic agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 131-157, January.
    4. Marcello Basili & Carlo Zappia, 2007. "The weight of argument and non-additive measures: a note," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 003, Department of Economic Policy, Finance and Development (DEPFID), University of Siena.
    5. Bastianello, Lorenzo & Chateauneuf, Alain, 2016. "About delay aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 62-77.
    6. Alberto Naudon & Matías Tapia, 2004. "Ignorance, Fixed Costs, and the Stock Market Participation Puzzle," Econometric Society 2004 Latin American Meetings 252, Econometric Society.
    7. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    8. Takao Asano & Hiroyuki Kojima, 2013. "Modularity and Monotonicity of Games," KIER Working Papers 871, Kyoto University, Institute of Economic Research.
    9. Takao Asano & Hiroyuki Kojima, 2015. "An axiomatization of Choquet expected utility with cominimum independence," Theory and Decision, Springer, vol. 78(1), pages 117-139, January.
    10. Roee Teper, 2009. "Time Continuity and Nonadditive Expected Utility," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 661-673, August.
    11. Alexander Ludwig & Alexander Zimper, 2004. "Rational Expectations and Ambiguity: A Comment on Abel," MEA discussion paper series 04066, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    12. Lorenzo Bastianello & Jos'e Heleno Faro, 2019. "Time discounting under uncertainty," Papers 1911.00370, arXiv.org, revised Mar 2020.
    13. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    14. Araujo, Aloisio & Novinski, Rodrigo & Páscoa, Mário R., 2011. "General equilibrium, wariness and efficient bubbles," Journal of Economic Theory, Elsevier, vol. 146(3), pages 785-811, May.
    15. Aloisio Araujo, 2015. "General equilibrium, preferences and financial institutions after the crisis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 217-254, February.
    16. Paolo Ghirardato & Daniele Pennesi, 2023. "Randomizing without randomness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1009-1037, May.
    17. Lorenzo Bastianello & José Heleno Faro, 2023. "Choquet expected discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May.
    18. Wakai, Katsutoshi, 2012. "An infinite-horizon model of nonmonotone utility smoothing," Economics Letters, Elsevier, vol. 116(2), pages 170-173.
    19. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    20. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2001. "Search under the Knightian Uncertainty," CIRJE F-Series CIRJE-F-112, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Choquet integral; comonotonicity; non-additive probabilities; capacities; cooperative games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

    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:kyo:wpaper:601. 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: Makoto Watanabe (email available below). General contact details of provider: https://edirc.repec.org/data/iekyojp.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.