A Game Theoretic Foundation of Competitive Equilibria with Adverse Selection

35 Pages Posted: 20 Oct 2012 Last revised: 22 Jun 2023

See all articles by Nick Netzer

Nick Netzer

University of Zurich

Florian Scheuer

Stanford University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: October 2012

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

Netzer, Nick and Scheuer, Florian, A Game Theoretic Foundation of Competitive Equilibria with Adverse Selection (October 2012). NBER Working Paper No. w18471, Available at SSRN: https://ssrn.com/abstract=2164595

Nick Netzer (Contact Author)

University of Zurich ( email )

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Zürich, CH-8006
Switzerland

Florian Scheuer

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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