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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18471.

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Date of creation: Oct 2012
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Publication status: published as 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, 05.
Handle: RePEc:nbr:nberwo:18471

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  1. Eckstein, Zvi & Eichenbaum, Martin & Peled, Dan, 1985. "Uncertain lifetimes and the welfare enhancing properties of annuity markets and social security," Journal of Public Economics, Elsevier, vol. 26(3), pages 303-326, April.
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  4. Pradeep Dubey & John Geanakoplos, 2002. "Competitive Pooling: Rothschild-Stiglitz Reconsidered," The Quarterly Journal of Economics, MIT Press, vol. 117(4), pages 1529-1570, November.
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  7. Theodoros M. Diasakos & Kostas Koufopoulos, 2011. "Efficient Nash Equilibrium under Adverse Selection," Carlo Alberto Notebooks 215, Collegio Carlo Alberto.
  8. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  9. Nick Netzer & Florian Scheuer, 2010. "Competitive Markets without Commitment," NajEcon Working Paper Reviews 814577000000000462, www.najecon.org.
  10. 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.
  11. Rasmusen, E. & Fernandez, L., 1993. "Perfectly Contestable Monopoly and Adverse Selection," Papers 93-016, Indiana - Center for Econometric Model Research.
  12. Spence, Michael, 1978. "Product differentiation and performance in insurance markets," Journal of Public Economics, Elsevier, vol. 10(3), pages 427-447, December.
  13. 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.
  14. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
  15. Pradeep Dubey & John Geanakoplos, 2001. "Competitive Pooling: Rothschild-Stiglitz Reconsidered," Cowles Foundation Discussion Papers 1346R2, Cowles Foundation for Research in Economics, Yale University, revised Feb 2002.
  16. Hajime Miyazaki, 1977. "The Rat Race and Internal Labor Markets," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 394-418, Autumn.
  17. Inderst, Roman & Wambach, Achim, 2001. "Competitive insurance markets under adverse selection and capacity constraints," European Economic Review, Elsevier, vol. 45(10), pages 1981-1992, December.
  18. Gale, Douglas, 1992. "A Walrasian Theory of Markets with Adverse Selection," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 229-55, April.
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Cited by:
  1. 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.
  2. Theodoros M. Diasakos & Kostas Koufopoulos, 2011. "Efficient Nash Equilibrium under Adverse Selection," Carlo Alberto Notebooks 215, Collegio Carlo Alberto.

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