IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2601.21275.html

Compromise by "multimatum"

Author

Listed:
  • Federico Echenique
  • Mat'ias N'u~nez

Abstract

We propose a solution and a mechanism for two-agent social choice problems with large (infinite) policy spaces. Our solution is an efficient compromise rule between the two agents, built on a common cardinalization of their preferences. Our mechanism, the multimatum, has the two players alternate in proposing sets of alternatives from which the other must choose. Our main result shows that the multimatum fully implements our compromise solution in subgame perfect Nash equilibrium. We demonstrate the power and versatility of this approach through applications to political economy, other-regarding preferences, and facility location.

Suggested Citation

  • Federico Echenique & Mat'ias N'u~nez, 2026. "Compromise by "multimatum"," Papers 2601.21275, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2601.21275
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2601.21275
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Myerson, Roger B, 1977. "Two-Person Bargaining Problems and Comparable Utility," Econometrica, Econometric Society, vol. 45(7), pages 1631-1637, October.
    2. Salvador Barberà & Danilo Coelho, 2022. "Compromising on compromise rules," RAND Journal of Economics, RAND Corporation, vol. 53(1), pages 95-112, March.
    3. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    4. Julien Combe & Olivier Tercieux & Camille Terrier, 2022. "The Design of Teacher Assignment: Theory and Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3154-3222.
    5. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    6. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    7. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    8. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    9. Bouacida, Elias & Foucart, Renaud, 2025. "Rituals of reason: Experimental evidence on the social acceptability of lotteries in allocation problems," Games and Economic Behavior, Elsevier, vol. 152(C), pages 23-36.
    10. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    11. Nejat Anbarci, 1993. "Noncooperative Foundations of the Area Monotonic Solution," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 245-258.
    12. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    13. Border Kim C. & Segal Uzi, 1994. "Dynamic Consistency Implies Approximately Expected Utility Preferences," Journal of Economic Theory, Elsevier, vol. 63(2), pages 170-188, August.
    14. T. Renee Bowen & Ying Chen & H?lya Eraslan, 2014. "Mandatory versus Discretionary Spending: The Status Quo Effect," American Economic Review, American Economic Association, vol. 104(10), pages 2941-2974, October.
    15. 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.
    16. Nikzad, Afshin, 2022. "Rank-optimal assignments in uniform markets," Theoretical Economics, Econometric Society, vol. 17(1), January.
    17. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    18. S. Nageeb Ali & Navin Kartik & Andreas Kleiner, 2023. "Sequential Veto Bargaining With Incomplete Information," Econometrica, Econometric Society, vol. 91(4), pages 1527-1562, July.
    19. Davis, Otto A. & Hinich, Melvin J. & Ordeshook, Peter C., 1970. "An Expository Development of a Mathematical Model of the Electoral Process," American Political Science Review, Cambridge University Press, vol. 64(2), pages 426-448, June.
    20. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
    21. Alberto Alesina & Guido Tabellini, 1990. "A Positive Theory of Fiscal Deficits and Government Debt," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 403-414.
    22. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
    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. Yakov Babichenko & Leonard J. Schulman, 2015. "Pareto Efficient Nash Implementation Via Approval Voting," Papers 1502.05238, arXiv.org, revised Mar 2017.
    2. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    3. 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.
    4. Miyagawa, Eiichi, 2002. "Subgame-perfect implementation of bargaining solutions," Games and Economic Behavior, Elsevier, vol. 41(2), pages 292-308, November.
    5. Lombardi, Michele & Yoshihara, Naoki, 2016. "Partially-honest Nash Implementation with Non-connected Honesty Standards," Discussion Paper Series 633, Institute of Economic Research, Hitotsubashi University.
    6. Troyan, Peter, 2024. "(Non-)obvious manipulability of rank-minimizing mechanisms," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    7. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    8. Peter Troyan, 2022. "Non-Obvious Manipulability of the Rank-Minimizing Mechanism," Papers 2206.11359, arXiv.org, revised Jun 2024.
    9. Michele Lombardi & Naoki Yoshihara, 2017. "Treading a Â…fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Working Papers SDES-2017-14, Kochi University of Technology, School of Economics and Management, revised Aug 2017.
    10. Lombardi, M. & Yoshihara, N., 2018. "Treading a fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Games and Economic Behavior, Elsevier, vol. 111(C), pages 203-216.
    11. Federico Echenique & Matías Núñez, 2025. "Price and Choose," American Economic Journal: Microeconomics, American Economic Association, vol. 17(2), pages 1-27, May.
    12. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    14. Federico Echenique & Matías Núñez, 2025. "Price and Choose," Post-Print hal-05511714, HAL.
    15. 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.
    16. Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 533-563, December.
    17. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-980, November.
    18. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.
    19. Marina Azzimonti & Laura Karpuska & Gabriel Mihalache, 2020. "Bargaining over Mandatory Spending and Entitlements," Department of Economics Working Papers 20-02, Stony Brook University, Department of Economics.
    20. Nejat Anbarci, 1997. "Noncooperative foundations for the kalai-smorodinsky and equal sacrifice solutions via prominence structures," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 25(4), pages 403-411, December.

    More about this item

    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:arx:papers:2601.21275. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.