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December 2006
View Faynzilberg, Peter S. Credible Forward Commitments and Risk-sharing Equilibria
It is shown that risk-sharing examined in Rothschild and Stiglitz (1976) has a perfect Nash equilibrium, which is unique, incentive-efficient and continuous in all parameters of the economy. Competition in individual markets of a perfectly competitive economy is generally imperfect and allows for cross-market subsidies. Contrary to the commonly accepted view, buyer's valuation of a contract cannot be identified with her valuation of consumption stipulated by that contract. A promise of future performance by a seller lacks credibility whenever its acceptance by buyers leads to a probable violation of seller's resource constraints. This renders vacuous threats to equilibrium that Rothschild and Stiglitz view as leading to extreme market failure.
May 2006
View Faynzilberg, Peter S. Competitive Insurance Markets I: The Concept and Efficiency of Equilibrium
Inter-firm rivalry and its impact on the stationarity of the economy are formalized in terms of selective efficiency that extends the Pareto and the Caldor-Hicks efficiency comparisons. Nash equilibrium of agents’ decision-making is shown to be sufficient for an economy to be in equilibrium. Conversely, the extant
practice of reliance on ad hoc “concepts of equilibrium” renders the resulting models overspecified. The ensuing loss of internal consistency explains the absence of a putative equilibrium in Rothschild and Stiglitz (1976), commonly interpreted as extreme market failure.View Faynzilberg, Peter S. Competitive Insurance Markets II: The Structure of Equilibrium and Comparative Statics
Under the conditions conjectured by Rothschild and Stiglitz (1976) as leading to extreme market failure, we show the existence of a unique incentive-efficient equilibrium. In terms of its sensitivity to the structure of the buyer population, this equilibrium may be flexible or rigid. Closed-form illustrations of equilibria and the solution methodology, which is based on the characterization of Nash equilibrium in terms of selective efficiency (Faynzilberg, 2003), are also provided.
April 200
5View Faynzilberg, Peter S. Equilibrium and the Scope of Trade in the ``Market'' for ``Lemons''
Under the conditions conjectured by Akerlof (1970) as leading to extreme market failure, we demonstrate the existence of equilibrium with trade. This equilibrium state is unique if buyers value goods strictly more than sellers, and the least-valued good is always traded in that state. Specializing to Akerlof's setting, we show that the least-valued good is the only one exchanged in the second-best equilibrium. Its value is known to all agents even when buyers are uninformed of the values of other commodities, and this good is sold at the first-best price.
May 2003
View
Faynzilberg, Peter S. Existence of Equilibria in
Competitive Insurance Markets,
in Financial Institutions and Services, Robert S.
Uh, Editor, Nova Science Publishers, 2005
Generalizing from the setting of Rothschild and Stiglitz (1976) to multi-segmented markets, we demonstrate the existence of a unique equilibrium in a risk-sharing economy with adverse selection. This equilibrium may be separating or partially pooling: in an economy with three types, for instance, the low- and the medium-risk buyer segments may be offered the same insurance policy.
In equilibrium, buyers' indirect utility decreases with their propensity for accident. When low-risk buyers are prevalent, sellers subsidize their operations across segments: they derive a positive profit in the low-risk segment and incur a loss of equal magnitude in the rest of the economy. This leaves high-risk buyers better off than under the first-best policy they purchase when sellers are perfectly informed.
In contrast to the putative equilibrium of the Rothschild-Stiglitz model, the second-best equilibrium depends on the structure of the buyer population and converges to the first-best of the corresponding homogeneous population as low-risk buyers become increasingly prevalent in the economy.