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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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    Cited by:

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    2. Alex Citanna & Paolo Siconolfi, 2022. "An incentive efficient market for mechanisms in large Akerlof economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 1-54, February.
    3. Pablo Kurlat & Florian Scheuer, 2021. "Signalling to Experts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 800-850.
    4. De Feo, Giuseppe & Hindriks, Jean, 2014. "Harmful competition in insurance markets," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 213-226.
    5. Dionne, Georges & Fombaron, Nathalie & Mimra, Wanda, 2023. "Adverse selection in insurance," Working Papers 23-5, HEC Montreal, Canada Research Chair in Risk Management.
    6. Kosenko, Andrew & Stiglitz, Joseph & Yun, Jungyoll, 2023. "Bilateral information disclosure in adverse selection markets with nonexclusive competition," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 144-168.
    7. 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.
    8. Theodoros M. Diasakos & Kostas Koufopoulos, 2011. "Efficient Nash Equilibrium under Adverse Selection," Carlo Alberto Notebooks 215, Collegio Carlo Alberto.
    9. Redouane Elkamhi & Latchezar Popov & Raunaq S. Pungaliya, 2023. "Financial maintenance covenants in bank loans," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1197-1255, November.
    10. 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).
    11. 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.
    12. Dosis, Anastasios, 2022. "Price caps and efficiency in markets with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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    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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