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Contract withdrawals and equilibrium in competitive markets with adverse selection

Author

Listed:
  • Wanda Mimra

    (ETH Zurich)

  • Achim Wambach

    (Centre for European Economic Research (ZEW) and University of Mannheim)

Abstract

In competitive common value adverse selection markets, existence of a pure strategy equilibrium is often justified by appealing to Wilson’s (J Econ Theory 16(2):167–207, 1977) concept of ‘anticipatory equilibrium.’ The anticipatory equilibrium is based on the notion that all market participants expect unprofitable contracts to be withdrawn. We present a model of individual contract withdrawals that captures the strategic process underlying the anticipatory equilibrium concept: We introduce an additional—endogenously ending—stage into the Rothschild and Stiglitz (Q J Econ 90(4):629–649, 1976) model in which initial contracts can be withdrawn repeatedly after observation of competitors’ contract offers and withdrawals. Individual contract withdrawal allows for a rich strategic interaction. We show that an equilibrium exists where consumers obtain their respective second-best efficient Miyazaki–Wilson–Spence (MWS) contracts. However, this equilibrium requires latent contracts on offer. Furthermore, any individually rational and incentive-compatible allocation that earns nonnegative profits on aggregate can be sustained as equilibrium allocation. We further allow for contract addition as in Riley’s (Econometrica 47(2):331–359, 1979) ‘reactive equilibrium.’ Allowing for contract addition does not change the set of possible outcomes.

Suggested Citation

  • Wanda Mimra & Achim Wambach, 2019. "Contract withdrawals and equilibrium in competitive markets with adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 875-907, June.
  • Handle: RePEc:spr:joecth:v:67:y:2019:i:4:d:10.1007_s00199-018-1101-4
    DOI: 10.1007/s00199-018-1101-4
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    1. Nick Netzer & Florian Scheuer, 2014. "A Game Theoretic Foundation Of Competitive Equilibria With Adverse Selection," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 399-422, May.
    2. Andrea Attar & Thomas Mariotti & François Salanié, 2011. "Nonexclusive Competition in the Market for Lemons," Econometrica, Econometric Society, vol. 79(6), pages 1869-1918, November.
    3. Adam Blandin & John H. Boyd & Edward C. Prescott, 2016. "Equilibrium with mutual organizations in adverse selection economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 3-13, June.
    4. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, Oxford University Press, vol. 90(4), pages 629-649.
    5. Pierre Picard, 2019. "Equilibrium in Insurance Markets With Adverse Selection When Insurers Pay Policy Dividends," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(4), pages 887-914, December.
    6. Crocker, Keith J. & Snow, Arthur, 1985. "The efficiency of competitive equilibria in insurance markets with asymmetric information," Journal of Public Economics, Elsevier, vol. 26(2), pages 207-219, March.
    7. Riley, John G, 1979. "Informational Equilibrium," Econometrica, Econometric Society, vol. 47(2), pages 331-359, March.
    8. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2014. "Nonexclusive competition under adverse selection," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Farinha Luz, Vitor, 2017. "Characterization and uniqueness of equilibrium in competitive insurance," Theoretical Economics, Econometric Society, vol. 12(3), September.
    10. Veronica Guerrieri & Robert Shimer & Randall Wright, 2010. "Adverse Selection in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 78(6), pages 1823-1862, November.
    11. Hellwig, Martin, 1987. "Some recent developments in the theory of competition in markets with adverse selection ," European Economic Review, Elsevier, vol. 31(1-2), pages 319-325.
    12. Engers, Maxim & Fernandez, Luis F, 1987. "Market Equilibrium with Hidden Knowledge and Self-selection," Econometrica, Econometric Society, vol. 55(2), pages 425-439, March.
    13. Jaynes, Gerald David, 1978. "Equilibria in monopolistically competitive insurance markets," Journal of Economic Theory, Elsevier, vol. 19(2), pages 394-422, December.
    14. Alberto Bisin & Piero Gottardi, 2006. "Efficient Competitive Equilibria with Adverse Selection," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 485-516, June.
    15. Pierre Picard, 2014. "Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 153-175, September.
    16. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
    17. Hajime Miyazaki, 1977. "The Rat Race and Internal Labor Markets," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 394-418, Autumn.
    18. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    19. Stefanie Stantcheva, 2014. "Optimal Income Taxation with Adverse Selection in the Labour Market," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 1296-1329.
    20. Wanda Mimra & Achim Wambach, 2014. "New Developments in the Theory of Adverse Selection in Competitive Insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 136-152, September.
    21. John G. Riley, 2001. "Silver Signals: Twenty-Five Years of Screening and Signaling," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 432-478, June.
    22. Szentes, Balázs, 2015. "Contractible contracts in common agency problems," LSE Research Online Documents on Economics 66071, London School of Economics and Political Science, LSE Library.
    23. Pradeep Dubey & John Geanakoplos, 2002. "Competitive Pooling: Rothschild-Stiglitz Reconsidered," The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1529-1570.
    24. Asheim, Geir B. & Nilssen, Tore, 1996. "Non-discriminating renegotiation in a competitive insurance market," European Economic Review, Elsevier, vol. 40(9), pages 1717-1736, December.
    25. Koufopoulos, Kostas & Kozhan, Roman, 2014. "Welfare-improving ambiguity in insurance markets with asymmetric information," Journal of Economic Theory, Elsevier, vol. 151(C), pages 551-560.
    26. Spence, Michael, 1978. "Product differentiation and performance in insurance markets," Journal of Public Economics, Elsevier, vol. 10(3), pages 427-447, December.
    27. Balázs Szentes, 2015. "Contractible Contracts in Common Agency Problems," Review of Economic Studies, Oxford University Press, vol. 82(1), pages 391-422.
    28. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, Oxford University Press, vol. 84(3), pages 488-500.
    29. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    30. Ania, Ana B. & Troger, Thomas & Wambach, Achim, 2002. "An evolutionary analysis of insurance markets with adverse selection," Games and Economic Behavior, Elsevier, vol. 40(2), pages 153-184, August.
    31. Kostas Koufopoulos & Roman Kozhan, 2016. "Optimal insurance under adverse selection and ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 659-687, October.
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    3. Saki Bigio & Liyan Shi, 2020. "Repurchase Options in the Market for Lemons," NBER Working Papers 27732, National Bureau of Economic Research, Inc.
    4. Levy, Yehuda John & Veiga, Andre, 2020. "On the existence of positive equilibrium profits in competitive screening markets," Games and Economic Behavior, Elsevier, vol. 124(C), pages 140-168.

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    More about this item

    Keywords

    Asymmetric information; Competitive insurance market; Contract withdrawal;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

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