A Game Theoretic Foundation of Competitive Equilibria With Adverse Selection

Netzer, Nick; Scheuer, Florian

doi:10.1111/iere.12054

Cited by 49 publications

(13 citation statements)

References 42 publications

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“…If the RS equilibrium does not exist, the MW contracts include a cross subsidisation from the low risk to the high-risk type. As our set-up is not exactly the same as in Netzer and Scheuer (2014), we prove these results for our set-up in the online Appendix. 17 The question is: does this characterisation of the 'perfect competition' outcome allow for q h \ 1?…”

Section: Fig 1 Incentive Compatibility Constraintssupporting

confidence: 53%

“…When the only separating equilibrium is broken by a pooling contract, an RS equilibrium does not exist. Wilson (1977) (also Miyazaki, 1977Spence, 1978;Netzer and Scheuer, 2014) offers a slightly different model of perfect competition in an insurance market where equilibrium always exists. The main difference between RS and Wilson (1977) is that Wilson uses an equilibrium notion where every firm expects that all contracts that become unprofitable due to the firm's offered contracts will be withdrawn immediately.…”

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

“…The main difference between RS and Wilson (1977) is that Wilson uses an equilibrium notion where every firm expects that all contracts that become unprofitable due to the firm's offered contracts will be withdrawn immediately. Netzer and Scheuer (2014) specify an extensive form game that generates this equilibrium as a subgame perfect equilibrium that is robust to the introduction ɛ > 0 withdrawal costs. We denote these contracts 'MW contracts'.…”

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

“…As shown by Miyazaki (1977) and Netzer and Scheuer (2014), MW contracts areadapted to our notationthe solution to the following optimisation problem: 16 max p h ;q h ;p l ;q l uðq l ; p l ; h l Þ ð P MW Þ subject to the constraints where / is the share of h h types in the population. The first two constraints are IC constraints.…”

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

“…Crosssubsidisation from h h to h l types is prohibited by (13). Netzer and Scheuer (2014) derive a number of properties of optimisation problem (P MW ). For us, the relevant properties are:…”

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

See 4 more Smart Citations

Health Insurance without Single Crossing: Why Healthy People have High Coverage

Boone

Schottmüller

2015

The Economic Journal

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Standard insurance models predict that people with high risks have high insurance coverage. It is empirically documented that people with high income have lower health risks and are better insured. We show that income differences between risk types lead to a violation of single crossing in an insurance model where people choose treatment intensity. We analyse different market structures and show the following: if insurers have market power, the violation of single crossing caused by income differences and endogenous treatment choice can explain the empirically observed outcome. Our results do not rely on differences in risk aversion between types.A well-documented problem in health insurance markets with voluntary insurance like the US is that people either have no insurance at all or are under-insured. 1 Standard insurance models -inspired by the seminal work of Rothschild and Stiglitz (1976; RS) and Stiglitz (1977) -predict that healthy people have less than perfect insurance or-in the extreme-no insurance at all. However, both popular accounts like Cohn (2007) and academic work like Schoen et al. (2008) show that people with low health status are over-represented in the group of uninsured and under-insured. 2 We develop a model to explain why sick people end up with too little (from a social point of view) or no insurance. We do this by adding two well-documented empirical observations to the RS model:(i) richer people tend to be healthier; and (ii) health is a normal good.Technically speaking, introducing the latter two effects can lead to a violation of single crossing in the model.There is another indication that the standard RS framework with single crossing does not capture reality in the health insurance sector well. The empirical literature that is based on RS does not unambiguously show that asymmetric information plays a role in health insurance markets. One would expect that people have private information about their health risks -think for example of preconditions, medical history of parents and other family members or lifestyle. However, some papers, like for We thank the editor (Martin W Cripps) and two anonymous referees of this JOURNAL for their suggestions. Comments by Cedric Argenton, Eric van Damme, Humberto Moreira, Florian Sch€ utt and seminar participants at Tilburg University are much appreciated. Financial support from the Dutch National Science Foundation (VICI 453.07.003) is gratefully acknowledged.1 In empirical studies, under-insurance is defined using indicators of financial risk. To illustrate, one definition of under-insurance used by Schoen et al. (2008) is 'out-of-pocket medical expenses for care amounted to 10% of income or more'. In our theoretical model, under-insurance refers to less than socially optimal/efficient insurance. 2 In the words of Schoen et al. (2008, p. 303): 'underinsurance rates were higher among adults with health problems than among healthier adults'.[ 1 ]

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Section: Fig 1 Incentive Compatibility Constraintssupporting

confidence: 53%

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

Section: Fig 1 Incentive Compatibility Constraintsmentioning

confidence: 99%

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Health Insurance without Single Crossing: Why Healthy People have High Coverage

Boone

Schottmüller

2015

The Economic Journal

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Optimal insurance under adverse selection and ambiguity aversion

Koufopoulos

Kozhan

2015

Econ Theory

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Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

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Contract withdrawals and equilibrium in competitive markets with adverse selection

Mimra

Wambach

2018

Econ Theory

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In competitive common value adverse selection markets, existence of a pure strategy equilibrium is often justified by appealing to Wilson's (J Econ Theory 16(2): 1977) concept of 'anticipatory equilibrium.' The anticipatory equilibrium is based on the notion that all market participants expect unprofitable contracts to be withdrawn. We present a model of individual contract withdrawals that captures the strategic process underlying the anticipatory equilibrium concept: We introduce an additional-endogenously ending-stage into the Rothschild and Stiglitz (Q J Econ 90(4):629-649, 1976) model in which initial contracts can be withdrawn repeatedly after observation of competitors' contract offers and withdrawals. Individual contract withdrawal allows for a rich strategic interaction. We show that an equilibrium exists where consumers obtain their respective second-best efficient Miyazaki-Wilson-Spence (MWS) contracts. However, this equilibrium requires latent contracts on offer. Furthermore, any individually rational and incentive-compatible allocation that earns nonnegative profits on aggregate can be sustained as equilibrium allocation. We further allow for contract addition as in Riley's (Econometrica 47(2):331-359, 1979) 'reactive equilibrium.' Allowing for contract addition does not change the set of possible outcomes.

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A Game Theoretic Foundation of Competitive Equilibria With Adverse Selection

Cited by 49 publications

References 42 publications

Health Insurance without Single Crossing: Why Healthy People have High Coverage

Health Insurance without Single Crossing: Why Healthy People have High Coverage

Optimal insurance under adverse selection and ambiguity aversion

Contract withdrawals and equilibrium in competitive markets with adverse selection

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