Economic Theory

, Volume 67, Issue 4, pp 875–907 | Cite as

Contract withdrawals and equilibrium in competitive markets with adverse selection

  • Wanda MimraEmail author
  • Achim Wambach
Research Article


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 The anticipatory equilibrium is based on the notion that all market participants expect unprofitable contracts to be withdrawn.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ending—stage into the Rothschild and Stiglitz (Q J Econ 90(4):629–649, 1976) model in which initial contracts can be withdrawn repeatedly after observation of competitors’ contract offers and withdrawals.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.


Asymmetric information Competitive insurance market Contract withdrawal 

JEL Classification

C72 D82 G22 L10 


  1. Akerlof, G.A.: The market for lemons: quality uncertainty and the market mechanism. Q. J. Econ. 84(3), 488–500 (1970)CrossRefGoogle Scholar
  2. Ales, L., Maziero, P.: Adverse selection and non-exclusive contracts. Working Paper (2013)Google Scholar
  3. Ania, A.B., Tröger, T., Wambach, A.: An evolutionary analysis of insurance markets with adverse selection. Games Econ. Behav. 40(2), 153–184 (2002)CrossRefGoogle Scholar
  4. Asheim, G.B., Nilssen, T.: Non-discriminating renegotiation in a competitive insurance market. Eur. Econ. Rev. 40(9), 1717–1736 (1996)CrossRefGoogle Scholar
  5. Attar, A., Mariotti, T., Salanié, F.: Non-exclusive competition in the market for lemons. Econometrica 79(6), 1869–1918 (2011)CrossRefGoogle Scholar
  6. Attar, A., Mariotti, T., Salanié, F.: Non-exclusive competition under adverse selection. Theor. Econ. 9, 1–40 (2014)CrossRefGoogle Scholar
  7. Bisin, A., Gottardi, P.: Efficient competitive equilibria with adverse selection. J. Polit. Econ. 114(3), 485–516 (2006)CrossRefGoogle Scholar
  8. Blandin, A., Boyd, J.H., Prescott, E.C.: Equilibrium with mutual organizations in adverse selection economies. Econ. Theory 62(1), 3–13 (2016)CrossRefGoogle Scholar
  9. Citanna, A., Siconolfi, P.: Incentive efficient price systems in large insurance economies with adverse selection. Int. Econ. Rev. 57, 1027–1056 (2015)CrossRefGoogle Scholar
  10. Crocker, K.J., Snow, A.: The efficiency of competitive equilibria in insurance markets with asymmetric information. J. Public Econ. 26(2), 207–219 (1985)CrossRefGoogle Scholar
  11. Dasgupta, P., Maskin, E.: The existence of equilibrium in discontinuous economic games, II: applications. Rev. Econ. Stud. 53(1), 27–41 (1986)CrossRefGoogle Scholar
  12. Diasakos, T., Koufopoulos, K.: (Neutrally) optimal mechanism under adverse selection: the canonical insurance problem. Working Paper (2015)Google Scholar
  13. Dubey, P., Geanakoplos, J.: Competitive pooling: Rothschild-Stiglitz reconsidered. Q. J. Econ. 117(4), 1529–1570 (2002)CrossRefGoogle Scholar
  14. Engers, M., Fernandez, L.: Market equilibrium with hidden knowledge and self-selection. Econometrica 55(2), 425–439 (1987)CrossRefGoogle Scholar
  15. Farinha Luz, V.: Characterization and uniqueness of equilibrium in competitive insurance. Theor. Econ. 12(3), 1349–1391 (2017)CrossRefGoogle Scholar
  16. Faynzilberg, P.S.: Credible forward commitments and risk-sharing equilibria. Mimeo (2006)Google Scholar
  17. Guerrieri, V., Shimer, R., Wright, R.: Adverse selection in competitive search equilibrium. Econometrica 78(6), 1823–1862 (2010)CrossRefGoogle Scholar
  18. Hellwig, M.: Some recent developments in the theory of competition in markets with adverse selection. Eur. Econ. Rev. 31(1–2), 319–325 (1987)CrossRefGoogle Scholar
  19. Inderst, R., Wambach, A.: Competitive insurance markets under adverse selection and capacity constraints. Eur. Econ. Rev. 45(10), 1981–1992 (2001)CrossRefGoogle Scholar
  20. Jaynes, G.D.: Equilibria in monopolistically competitive insurance markets. J. Econ. Theory 19(2), 394–422 (1978)CrossRefGoogle Scholar
  21. Koufopoulos, K., Kozhan, R.: Welfare-improving ambiguity in insurance markets with asymmetric information. J. Econ. Theory 151, 551–560 (2014)CrossRefGoogle Scholar
  22. Koufopoulos, K., Kozhan, R.: Optimal insurance under adverse selection and ambiguity aversion. Econ. Theory 62(4), 659–687 (2016)CrossRefGoogle Scholar
  23. Lacker, J.M., Weinberg, J.A.: Coalition-proof allocations in adverse-selection economies. Geneva Pap. Risk Insur. Theory 24(1), 5–17 (1999)CrossRefGoogle Scholar
  24. Mimra, W., Wambach, A.: New developments in the theory of adverse selection in competitive insurance. Geneva Risk Insur. Rev. 39(2), 136–152 (2014)CrossRefGoogle Scholar
  25. Mimra, W., Wambach, A.: Endogenous insolvency in the Rothschild-Stiglitz model. J. Risk Insur. (2017). Google Scholar
  26. Miyazaki, H.: The rat race and internal labor markets. Bell J. Econ. 8(2), 394–418 (1977)CrossRefGoogle Scholar
  27. Netzer, N., Scheuer, F.: A game theoretic foundation of competitive equilibria with adverse selection. Int. Econ. Rev. 55(2), 399–422 (2014)CrossRefGoogle Scholar
  28. Picard, P.: Participating insurance contracts and the Rothschild–Stiglitz equilibrium puzzle. Geneva Risk Insur. Rev. 39(2), 153–175 (2014)CrossRefGoogle Scholar
  29. Picard, P.: Equilibrium in insurance markets with adverse selection when insurers pay policy dividends. Working Paper (2016)Google Scholar
  30. Riley, J.G.: Informational equilibrium. Econometrica 47(2), 331–359 (1979)CrossRefGoogle Scholar
  31. Riley, J.G.: Silver signals: twenty-five years of screening and signaling. J. Econ. Lit. 39(2), 432–478 (2001)CrossRefGoogle Scholar
  32. Rosenthal, R.W., Weiss, A.: Mixed-strategy equilibrium in a market with asymmetric information. Rev. Econ. Stud. 51(2), 333–342 (1984)CrossRefGoogle Scholar
  33. Rothschild, M., Stiglitz, J.: Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. Q. J. Econ. 90(4), 629–649 (1976)CrossRefGoogle Scholar
  34. Spence, M.: Product differentiation and performance in insurance markets. J. Public Econ. 10(3), 427–447 (1978)CrossRefGoogle Scholar
  35. Stantcheva, S.: Optimal income taxation with adverse selection in the labour market. Rev. Econ. Stud. 81, 1296–1329 (2014)CrossRefGoogle Scholar
  36. Szentes, B.: Contractible contracts in common agency problems. Rev. Econ. Stud. 82(1), 391–422 (2015)CrossRefGoogle Scholar
  37. Wilson, C.: A model of insurance markets with incomplete information. J. Econ. Theory 16(2), 167–207 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center of Economic ResearchETH ZurichZürichSwitzerland
  2. 2.Centre for European Economic Research (ZEW) and University of MannheimMannheimGermany

Personalised recommendations