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A game theoretic foundation of competitive equilibria with adverse selection


Netzer, Nick; Scheuer, Florian (2012). A game theoretic foundation of competitive equilibria with adverse selection. NBER working paper series 18471, National Bureau of Economic Research.

Abstract

We construct a fully specified extensive form game that aptures competitive markets with adverse selection. In articular, 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.

Abstract

We construct a fully specified extensive form game that aptures competitive markets with adverse selection. In articular, 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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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Language:English
Date:October 2012
Deposited On:18 Dec 2012 09:59
Last Modified:20 Sep 2018 03:36
Series Name:NBER working paper series
Number of Pages:35
OA Status:Closed
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.nber.org/papers/w18471

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