Identification of Insurance Models with Multidimensional Types

2018 ◽  
Author(s):  
Gaurab Aryal ◽  
Isabelle Perrigne ◽  
Quang Vuong
Keyword(s):  
Multidimensional Types

scholarly journals Product Design in Selection Markets *

2016 ◽  
Vol 131 (2) ◽  
pp. 1007-1056 ◽  
Author(s):  
André Veiga ◽  
E. Glen Weyl
Keyword(s):  
Consumer Surplus ◽  
Insurance Markets ◽  
Social Planner ◽  
Endogenous Quality ◽  
Health Insurance Markets ◽  
Product Features ◽  
Marginal Willingness To Pay ◽  
Multidimensional Types ◽  
Simple Ratio ◽  
The Cost

Abstract In selection markets, where the cost of serving consumers is heterogeneous and noncontractible, nonprice product features allow a firm to sort profitable from unprofitable consumers. An example of this “sorting by quality” is the use of down payments to dissuade borrowers who are unlikely to repay. We study a model in which consumers have multidimensional types and a firm offers a single product of endogenous quality, as in Spence (1975) . These two ingredients generate a novel sorting incentive in a firm’s first-order condition for quality, which is a simple ratio. The denominator is marginal consumer surplus, a measure of market power. The numerator is the covariance, among marginal consumers, between marginal willingness to pay for quality and cost to the firm. We provide conditions under which this term is signed and contrast the sorting incentives of a profit-maximizer and a social planner. We then use this characterization to quantify the importance of sorting empirically in subprime auto lending, analytically sign its impact in a model of add-on pricing, and calibrate optimal competition policy in health insurance markets.

Optimal auctions with multidimensional types and the desirability of exclusion

2013 ◽  
Vol 49 (1) ◽  
pp. 106-110
Author(s):  
Paulo Klinger Monteiro ◽  
Frank H. Page ◽  
Benar fux Svaiter
Keyword(s):  
Optimal Auctions ◽  
Multidimensional Types

scholarly journals Efficient multiunit auctions for normal goods

2020 ◽  
Vol 15 (1) ◽  
pp. 361-413 ◽  
Author(s):  
Brian Baisa
Keyword(s):  
Incentive Compatibility ◽  
Dominant Strategy ◽  
Impossibility Theorem ◽  
Budget Balance ◽  
Auction Design ◽  
Vickrey Auction ◽  
Multiunit Auctions ◽  
Private Values ◽  
Multidimensional Types ◽  
Normal Goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

scholarly journals Equivalence of Stochastic and Deterministic Mechanisms

Econometrica ◽  
2019 ◽  
Vol 87 (4) ◽  
pp. 1367-1390 ◽  
Author(s):  
Yi-Chun Chen ◽  
Wei He ◽  
Jiangtao Li ◽  
Yeneng Sun
Keyword(s):  
Mechanism Design ◽  
Type Distribution ◽  
Incentive Compatible ◽  
Monetary Transfers ◽  
Ex Ante ◽  
Finite Set ◽  
Multidimensional Types ◽  
Social Surplus ◽  
Interdependent Valuations ◽  
Incentive Compatible Mechanism

We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.

Efficient Constrained Combinatorial Auctions

2016 ◽  
Vol 18 (03) ◽  
pp. 1650007
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Necessary Conditions ◽  
Dominant Strategy ◽  
Single Item ◽  
Constrained Efficiency ◽  
Incentive Compatible ◽  
Sufficient And Necessary Conditions ◽  
Multidimensional Types ◽  
The Individual ◽  
Efficient Mechanisms

The seminal work by Green and Laffont [(1977) characterization of satisfactory mechanisms for the revelation of preferences for public goods, Econometrica 45, 427–438] shows that efficient mechanisms with Vickrey–Clarke–Groves prices satisfy the properties of dominant-strategy incentive compatible (DSIC) and individually rational in the quasilinear utilities model. Nevertheless in many real-world situations some players have a gap between their willingness to pay and their ability to pay, i.e., a budget. We show that once budgets are integrated into the model then Green and Laffont’s theorem ceases to apply. More specifically, we show that even if only a single player has budget constraints then there is no deterministic efficient mechanism that satisfies the individual rationality and DSIC properties. Furthermore, in a quasilinear utilities model with [Formula: see text] nonidentical items and [Formula: see text] players with multidimensional types, we characterize the sufficient and necessary conditions under which Green and Laffont’s theorem holds in the presence of budget-constrained players. Interestingly our characterization is similar in spirit to that of Maskin [(2000) Auctions, development and privatization: Efficient auctions with liquidity-constrained buyers, Eur. Econ. Rev. 44, 667–681] for Bayesian single-item constrained-efficiency auctions.

Dictatorial Mechanisms in Constrained Combinatorial Auctions

2013 ◽  
Vol 13 (1) ◽  
pp. 363-380 ◽  
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Dominant Strategy ◽  
Combinatorial Auctions ◽  
Budget Constraints ◽  
Basic Properties ◽  
Incentive Compatible ◽  
Private Values ◽  
Multidimensional Types ◽  
Possibility Space ◽  
Pareto Efficient ◽  
Strategy Incentive

AbstractWe study the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient combinatorial auctions in a model with two players and two nonidentical items (four outcomes). Our model has multidimensional types, private values, nonnegative prices, and quasilinear preferences for the players with one relaxation – the players are subject to publicly known budget constraints. We show that the space we study essentially includes one type of mechanisms: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient. The mechanisms in the autocratic families are identical except for two to three price parameters that differentiate them.

Autocratic Mechanisms: A Form of Dictatorship in Constrained Combinatorial Auctions

2015 ◽  
Vol 17 (04) ◽  
pp. 1550010 ◽  
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Pareto Optimality ◽  
Dominant Strategy ◽  
Combinatorial Auctions ◽  
Pareto Optimal ◽  
Basic Properties ◽  
Incentive Compatible ◽  
Welfare Maximization ◽  
Private Values ◽  
Multidimensional Types ◽  
Strategy Incentive

We characterize the space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions where efficiency is not required. We examine a model with two players and k nonidentical items (2k outcomes), multidimensional types, private values, non-negative prices, and quasilinear preferences for the players with one relaxation — the players are subject to publicly-known budget constraints. We show that if it is publicly known that the players value the bundles more than the smaller of their budgets then the studied space includes one type of mechanism: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. Interestingly the above basic properties are a weaker requirement than it may initially appear, as the property of Pareto optimality in our model of budget-constrained players and non-negative prices do not coincide with welfare maximization, i.e., efficiency as such is a much weaker requirement.

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