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A Game Theoretic Foundation of Competitive Equilibria with Adverse Selection

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  • Nick Netzer
  • Florian Scheuer

Abstract

We construct a fully specified extensive form game that captures competitive markets with adverse selection. In particular, it allows firms to offer any finite set of contracts, so that cross-subsidization is not ruled out. Moreover, firms can withdraw from the market after initial contract offers have been observed. We show that a subgame perfect equilibrium always exists and that, in fact, when withdrawal is costless, the set of subgame perfect equilibrium outcomes may correspond to the entire set of feasible contracts. We then focus on robust equilibria that exist both when withdrawal costs are zero and when they are arbitrarily small but strictly positive. We show that the Miyazaki-Wilson contracts are the unique robust equilibrium outcome of our game. This outcome is always constrained efficient and involves cross-subsidization from low to high risk agents that is increasing in the share of low risks in the population under weak conditions on risk preferences.

Suggested Citation

  • Nick Netzer & Florian Scheuer, 2012. "A Game Theoretic Foundation of Competitive Equilibria with Adverse Selection," NBER Working Papers 18471, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18471
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    References listed on IDEAS

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    Cited by:

    1. von Siemens, Ferdinand A. & Kosfeld, Michael, 2014. "Team production in competitive labor markets with adverse selection," European Economic Review, Elsevier, vol. 68(C), pages 181-198.
    2. Theodoros M. Diasakos & Kostas Koufopoulos, 2011. "Efficient Nash Equilibrium under Adverse Selection," Carlo Alberto Notebooks 215, Collegio Carlo Alberto.
    3. Farinha Luz, Vitor, 2017. "Characterization and uniqueness of equilibrium in competitive insurance," Theoretical Economics, Econometric Society, vol. 12(3), September.
    4. Schumacher, Heiner, 2016. "Insurance, self-control, and contract flexibility," European Economic Review, Elsevier, vol. 83(C), pages 220-232.
    5. Anastasios Dosis, 2016. "Investment, Adverse Selection and Optimal Redistributive Taxation," Working Papers hal-01285163, HAL.
    6. Georges Dionne & Casey Rothschild, 2014. "Economic Effects of Risk Classification Bans," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 184-221, September.
    7. Bannier, Christina E. & Feess, Eberhard & Packham, Natalie, 2014. "Incentive schemes, private information and the double-edged role of competition for agents," CFS Working Paper Series 475, Center for Financial Studies (CFS).
    8. Dosis, Anastasios, 2017. "Nash equilibrium in competitive insurance," Economics Letters, Elsevier, vol. 152(C), pages 5-8.
    9. 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.
    10. Anastasios Dosis, 2016. "An Efficient Mechanism for Competitive Markets with Adverse Selection," Working Papers hal-01282772, HAL.
    11. Dosis, Anastasios, 2016. "Investment, Adverse Selection and Optimal Redistributive Taxation," ESSEC Working Papers WP1605, ESSEC Research Center, ESSEC Business School.
    12. 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.
    13. repec:eee:mateco:v:75:y:2018:i:c:p:140-149 is not listed on IDEAS
    14. Florian Scheuer & Kent Smetters, 2014. "Could a Website Really Have Doomed the Health Exchanges? Multiple Equilibria, Initial Conditions and the Construction of the Fine," NBER Working Papers 19835, National Bureau of Economic Research, Inc.
    15. Dosis, Anastasios, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," ESSEC Working Papers WP1607, ESSEC Research Center, ESSEC Business School.
    16. De Feo, Giuseppe & Hindriks, Jean, 2014. "Harmful competition in insurance markets," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 213-226.
    17. Andrew Glover & Dean Corbae, 2015. "A Simple Dynamic Theory of Credit Scores Under Adverse Selection," 2015 Meeting Papers 1265, Society for Economic Dynamics.
    18. Anastasios Dosis, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," Working Papers hal-01285188, HAL.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • H1 - Public Economics - - Structure and Scope of Government
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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