Following the seminal work by Arrow (1963), the notion of information asymmetry have by now been recognized as a cornerstone of modern insurance theory. Two focal cases have so far attracted particular attention from insurance economists. The concept of adverse selection refers to situations where, before the contract is signed, one party (in general the insured agent) has an information advantage upon the other. In most models, it is assumed that clients know better their own risk than insurance companies; the latter may then use deductible as a way of separating individuals with different riskiness. Moral hazard, on the other hand, occurs when the outcome of the relationship (here, the occurrence of an accident or a claim) depends, in a stochastic way, on a decision that is privately made by one party and not observable by the other. Typically, the insured party may choose to make an effort that is costly to her, but reduces her risk. In this context, full insurance generally leads to suboptimal outcomes, because it provides no incentive to reduce accident probabilities.
The effects of asymmetric information upon competition between insurers have been investigated in a number of papers, following the seminal contributions by Akerlof (1970), Rothschild and Stiglitz (1976) and Wilson (1977). Under adverse selection, equilibria a la Rothschild-Stiglitz may fail to exist; moreover, when they do, they may not be Pareto efficient, even among the subset of contracts that are compatible with the existing information asymmetry (second best efficiency). The properties of competitive equilibria under moral hazard, on the other hand, strongly depend on whether contracts are exclusive (i.e., the insurer may prohibit the acquisition of another contract by his clients) or not. With exclusivity, equilibria do exist in general, and are second best efficient, at least in a one commodity setting (see for instance Prescott and Townsend (1984)).