An example of non-existence of Riley equilibrium in markets with adverse selection

Rothschild and Stiglitz [1976] proposed a model of a competitive market with adverse selection and showed that a (pure strategy) Nash equilibrium may not exist. Among the solutions proposed to deal with this problem, a particularly influential one is the notion of Riley (or reactive) equilibrium [Riley, 1979]. We give an example that shows that a Riley equilibrium may not exist if consumers are not ordered

The trade-off between incentives and endogenous risk

Standard models of moral hazard predict a negative relationship between risk and incentives, but the empirical work has not confirmed this prediction. In this paper, we propose a model with adverse selection followed by moral hazard, where effort and the degree of risk aversion are private information of an agent who can control the mean and the variance of profits. For a given contract, more risk-averse agents supply more effort in risk reduction. If the marginal utility of incentives decreases with risk aversion, more risk-averse agents prefer lower-incentive contracts; thus, in the optimal contract, incentives are positively correlated with endogenous risk. In contrast, if risk aversion is high enough, the possibility of reduction in risk makes the marginal utility of incentives increasing in risk aversion and, in this case, risk and incentives are negatively related.Incentives, non-monotone contracts, single-crossing property.

The trade-off between incentives and endogenous risk

Standard models of moral hazard predict a negative relationship between risk and incentives, but the empirical work has not confirmed this prediction. In this paper, we propose a model with adverse selection followed by moral hazard, where effort and the degree of risk aversion are private information of an agent who can control the mean and the variance of profits. For a given contract, more risk-averse agents supply more effort in risk reduction. If the marginal utility of incentives decreases with risk aversion, more risk-averse agents prefer lower-incentive contracts; thus, in the optimal contract, incentives are positively correlated with endogenous risk. In contrast, if risk aversion is high enough, the possibility of reduction in risk makes the marginal utility of incentives increasing in risk aversion and, in this case, risk and incentives are negatively relatedIncentives, non-monotone contracts, single-crossing property.

Sequential versus Static Screening: An equivalence result

Abstract We show that the sequential screening model is equivalent to the standard static screening model. We use this insight to shed new light on the relation between static and dynamic screening models

Decomposable Principal-Agent Problems

This paper investigates conditions under which the adverse selection principal-agent problem can be decomposed into a collection of pointwise maximization problems. The analysis uses an extension of the type assignment approach to optimal nonuniform pricing, pioneered by Goldman, Leland and Sibley (1984), to derive simple sufficient conditions under which such a decomposition is possible. These conditions do not preclude optimal bunching that arises because virtual surplus functions violate the single-crossing property or participation constraints bind at interior types.

Procurement with Specialized Firms

This paper analyzes optimal procurement mechanisms in a setting where the procurement agency has incomplete information concerning the firms’ cost functions and cares about quality as well as price. Low type firms are cheaper than high type firms in providing low quality but more expensive when providing high quality. Hence, each type is specialized in a certain quality level. We show that this specialization leads to a bunching of types on profits, i.e. a range of firms with different cost functions receives zero profits and therefore no informational rents. If first best welfare is monotone in the efficiency parameter, the optimal mechanism can be implemented by a simple auction. If first best welfare is U-shaped in type, the optimal mechanism is not efficient in the sense that types providing a lower second best welfare win against types providing a higher second best welfare.procurement;specialization;deregulation