Trading under Asymmetric Information: Positive and Normative Implications

We study trading situations in which several principals on one side of the market compete to serve privately informed agents on the other side. In such ‘generalized screening’ settings, competitors may post mechanisms instead of prices, and the enforceability and the efficiency of the contractual relationships become difficult to evaluate. We revisit these issues, focusing on three applications: bilateral (or multilateral) trade, where all traders have private information, auctions and insurance, where incomplete information is one-sided. In the first part, as a benchmark, we focus on the standard mechanism design approach with only one principal, the “mechanism designer", and we rely on the revelation principle as a device to characterize equilibrium out- comes. Even then, first-best optimality, combined with Bayesian incentive compatibility and interim individual rationality might be difficult to obtain, as illustrated by Myerson and Satterthwaite (1983) impossibility result, for- mulated for risk-neutral traders with independent beliefs. In auctions, if the buyers types are correlated a la Cremer and McLean (1985,1988), this impos- sibility can be bypassed and the seller can extract the whole surplus. In the more general multilateral trade setting, a simple modification of a condition provided by d’Aspremont and Gerard-Varet (1982) allows to implement any distribution of the surplus (Kosenok and Severinov, 2008). However, under risk-aversion, only second-best outcomes can be implemented, as originally shown by Stiglitz (1977) for the monopolistic case, and by Crocker and Snow (1985) for the competitive one. In the second part, we consider a class of extensive form games in which several principals (with no private information) compete over mechanisms in the presence of privately informed agents. Applying the standard reve- lation principle becomes problematic, as first pointed out by Peck (1997): there exist equilibrium outcomes that can be supported by general commu- nication mechanisms, but not by simple direct ones. We revisit a relevant implication of this impossibility, i.e. the recent folk-theorem-like result of Yamashita (2010): if there are at least three agents, a large set of incentive compatible allocations can be supported at equilibrium. For the result to hold, principals have to rely on message spaces that are larger than the cor- responding agentsO type spaces. In the single agent (or common agency) case, the equilibrium analysis can be further simplified using the delegation principle (Peters, 2001, Martimort and Stole, 2002). In this context, we stress the key role played by the possibility to enforce exclusivity clauses. In standard exclusive competition settings (as Rothchild and Stiglitz, 1976), if a pure strategy equilibrium exists, it is second-best efficient (Crocker and Snow, 1985). This is no longer true under nonexclusive competition. In this case, the possibility to complement his rivals’ offers, creates new strategic opportunities for sellers, and crucially modifies equilibrium outcomes: Attar et al. (2014) establish that, in any pure strategy equilibrium, at most one type of agent is actively trading. The impossibility to enforce exclusive trad- ing may further restrict the set of incentive feasible allocations. The recent work of Attar et al. (2016b) characterizes the constraints faced by a planner who does not have access to agents’ private information, and cannot prevent agents’ from engaging in further trades with sellers. They show that this side-trading opportunity dramatically restricts the set of allocations that are available to a planner. As a matter of fact there is only one incentive com- patible allocation that is robust to the possibility of sellers’ side trades. This prevents any redistribution between different types of (privately informed) buyers.