(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)">
Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cdl/ucsdec/qt1fb0j67c.html
   My bibliography  Save this paper

Starting small in project choice: A discrete-time setting with a continuum of types

Author

Listed:
  • Hua, Xiameng
  • Watson, Joel
Abstract
We add to the literature on long-term relationships with variable stakes and incomplete information by analyzing a discrete-time trust game between a principal and agent, with a continuum of types. In each period the principal selects the level of a project and the agent then decides whether to cooperate or betray; payoffs in the period scale with the level. The agent's benefit of betraying is privately known. The discrete-time framework allows for analysis of renegotiation in terms of an internal consistency condition that compares actual equilibria in the continuation of the game from any period, improving on the prior literature. Our condition assumes the principal has full power to alter the equilibrium selection. Our main result shows that the resulting perfect Bayesian equilibria converge as the period length shrinks to zero, and we provide a closed-form solution. In equilibrium, the relationship starts small and the level gradually rises until it reaches its maximum; cooperation is viable regardless of the type distribution.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hua, Xiameng & Watson, Joel, 2022. "Starting small in project choice: A discrete-time setting with a continuum of types," University of California at San Diego, Economics Working Paper Series qt1fb0j67c, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt1fb0j67c
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/1fb0j67c.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James M. Malcomson, 2016. "Relational Incentive Contracts With Persistent Private Information," Econometrica, Econometric Society, vol. 84, pages 317-346, January.
    2. Ignatius J. Horstmann & James R. Markusen, 2018. "Learning to sell in new markets: A preliminary analysis of market entry by a multinational firm," Review of International Economics, Wiley Blackwell, vol. 26(5), pages 1040-1052, November.
    3. Watson, Joel, 2002. "Starting Small and Commitment," Games and Economic Behavior, Elsevier, vol. 38(1), pages 176-199, January.
    4. Ausubel, Lawrence M & Deneckere, Raymond J, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Econometrica, Econometric Society, vol. 57(3), pages 511-531, May.
    5. Larry M. Ausubel & Raymond J. Deneckere, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Levine's Working Paper Archive 201, David K. Levine.
    6. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    7. Horstmann, Ignatius J & Markusen, James R, 1996. "Exploring New Markets: Direct Investment, Contractual Relations and the Multinational Enterprise," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(1), pages 1-19, February.
    8. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    9. Rauch, James E. & Watson, Joel, 2003. "Starting small in an unfamiliar environment," International Journal of Industrial Organization, Elsevier, vol. 21(7), pages 1021-1042, September.
    10. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    11. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in Perturbed Repeated Games," Journal of Economic Theory, Elsevier, vol. 69(2), pages 387-410, May.
    12. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 491-519.
    13. Martin W. Cripps & Jonathan P. Thomas, 2003. "Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 433-462, August.
    14. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
    15. Gompers, Paul A, 1995. "Optimal Investment, Monitoring, and the Staging of Venture Capital," Journal of Finance, American Finance Association, vol. 50(5), pages 1461-1489, December.
    16. Joel Watson, 2013. "Contract and Game Theory: Basic Concepts for Settings with Finite Horizons," Games, MDPI, vol. 4(3), pages 1-40, August.
    17. Pierpaolo Battigalli & Joel Watson, 1997. "On "Reputation" Refinements with Heterogeneous Beliefs," Econometrica, Econometric Society, vol. 65(2), pages 369-374, March.
    18. Maoliang Ye & Jie Zheng & Plamen Nikolov & Sam Asher, 2020. "One Step at a Time: Does Gradualism Build Coordination?," Management Science, INFORMS, vol. 66(1), pages 113-129, January.
    19. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    20. Sylvain Chassang, 2010. "Building Routines: Learning, Cooperation, and the Dynamics of Incomplete Relational Contracts," American Economic Review, American Economic Association, vol. 100(1), pages 448-465, March.
    21. Tian, Xuan, 2011. "The causes and consequences of venture capital stage financing," Journal of Financial Economics, Elsevier, vol. 101(1), pages 132-159, July.
    22. Atakan, Alp & Koçkesen, Levent & Kubilay, Elif, 2020. "Starting small to communicate," Games and Economic Behavior, Elsevier, vol. 121(C), pages 265-296.
    23. HART, Sergiu, 1985. "Nonzerosum two-person repeated games with incomplete information," LIDAM Reprints CORE 636, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. James Andreoni & Michael A. Kuhn & Larry Samuelson, 2019. "Building rational cooperation on their own: Learning to start small," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(5), pages 812-825, October.
    25. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    26. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
    27. Joel Sobel, 1985. "A Theory of Credibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 557-573.
    28. Rafael Rob & Arthur Fishman, 2005. "Is Bigger Better? Customer Base Expansion through Word-of-Mouth Reputation," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 1146-1175, October.
    29. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    30. David A. Miller & Joel Watson, 2013. "A Theory of Disagreement in Repeated Games With Bargaining," Econometrica, Econometric Society, vol. 81(6), pages 2303-2350, November.
    31. Kranton, Rachel E, 1996. "The Formation of Cooperative Relationships," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 12(1), pages 214-233, April.
    32. Watson, Joel, 1999. "Starting Small and Renegotiation," Journal of Economic Theory, Elsevier, vol. 85(1), pages 52-90, March.
    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. Fabienne Schneider & Remo Taudien, 2024. "Credit and Anonymity," Working Papers 24.04, Swiss National Bank, Study Center Gerzensee.

    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. Joel Watson, 2021. "Theoretical Foundations of Relational Incentive Contracts," Annual Review of Economics, Annual Reviews, vol. 13(1), pages 631-659, August.
    2. Kartal, Melis & Müller, Wieland & Tremewan, James, 2021. "Building trust: The costs and benefits of gradualism," Games and Economic Behavior, Elsevier, vol. 130(C), pages 258-275.
    3. Rauch, James E. & Watson, Joel, 2003. "Starting small in an unfamiliar environment," International Journal of Industrial Organization, Elsevier, vol. 21(7), pages 1021-1042, September.
    4. Fischer, Christian, 2020. "Optimal payment contracts in trade relationships," MPRA Paper 101956, University Library of Munich, Germany.
    5. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    6. David Martimort & Aggey Semenov & Lars Stole, 2017. "A Theory of Contracts with Limited Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 816-852.
    7. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    8. Wei, Dong, 2019. "A model of trust building with anonymous re-matching," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 311-327.
    9. James M. Malcomson, 2012. "Relational Incentive Contracts [The Handbook of Organizational Economics]," Introductory Chapters,, Princeton University Press.
    10. Heidi Gjertsen & Theodore Groves & David A Miller & Eduard Niesten & Dale Squires & Joel Watson, 2021. "Conservation Agreements: Relational Contracts with Endogenous Monitoring," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 37(1), pages 1-40.
    11. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
    12. Marina Halac, 2012. "Relational Contracts and the Value of Relationships," American Economic Review, American Economic Association, vol. 102(2), pages 750-779, April.
    13. Pei, Harry, 2023. "Repeated communication with private lying costs," Journal of Economic Theory, Elsevier, vol. 210(C).
    14. Heidi Gjertsen & Theodore Groves & David A. Miller & Eduard Niesten & Dale Squires & Joel Watson, 2014. "A Contract-theoretic Model of Conservation Agreements," World Scientific Book Chapters, in: Kaddour Hadri & William Mikhail (ed.), Econometric Methods and Their Applications in Finance, Macro and Related Fields, chapter 15, pages 425-455, World Scientific Publishing Co. Pte. Ltd..
    15. Caroline Muthoni Muchina & Barrack Okello, 2016. "Influence of Personal Selling on Brand Performance of Retail Shoe Companies in Nairobi Central Business District," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 6(5), pages 1-14, May.
    16. Christian Fischer‐Thöne, 2023. "Optimal Payment Contracts In Trade Relationships," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1649-1683, November.
    17. Brown, Martin & Serra-García, Marta, 2014. "The Threat of Exclusion and Implicit Contracting," Working Papers on Finance 1407, University of St. Gallen, School of Finance, revised Jun 2016.
    18. Martin Brown & Marta Serra-Garcia, 2017. "The Threat of Exclusion and Implicit Contracting," Management Science, INFORMS, vol. 63(12), pages 4081-4100, December.
    19. Furusawa, Taiji & Kawakami, Toshikazu, 2008. "Gradual cooperation in the existence of outside options," Journal of Economic Behavior & Organization, Elsevier, vol. 68(2), pages 378-389, November.
    20. Luca Anderlini & Leonardo Felli, 1998. "Costly Bargaining and Renegotiation - (Now published in Econometrica, 69(4) (March 2001), pp. 377-411.)," STICERD - Theoretical Economics Paper Series 361, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    More about this item

    Keywords

    Economics; Applied Economics; Economic Theory; Project choice; Principal-agent; Renegotiation; Starting small; Gradualism; Perfect Bayesian equilibrium; Other Economics; Applied economics; Economic theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

    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:cdl:ucsdec:qt1fb0j67c. 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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/deucsus.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.