Adverse selection: general model and applications.

Summary The subject of my thesis is a continuation of the principal-agent literature with adverse selection, in insurance, we study a more general model than the Rothschild-Stiglitz model, assuming only the continuity of the agents' preferences and the semi-continuity of the principals' profit functions. This model retains certain analogies with the standard model, and in particular the existence of a dominant revealing mechanism. But it allows us to obtain a multiplicity of equilibria, or even a continuum, whereas the standard model gives only a single equilibrium. The existence of new types of equilibrium in which the two agents obtain contracts that are indifferent to each other is emphasized. This eventuality imposes to distinguish between nash equilibria in contracts and in schedules. These results are obtained from a detailed analysis of the properties of the revealing mechanisms. We finally show, under the hypotheses of quasi-concavity of the utility and profit functions of the agents, that a separating equilibrium always exists for at least a certain average composition of the population. A second line of research applies the above general model to several specific economies. To this end, we develop a mathematical algorithm that converges to the contracted equilibrium that dominates in a pareto sense all equilibria in the model. The double sequence of individually profitable contracts that we construct, starting from the top-ranking contracts, and, by successive bullying of the agents whose contract induces jealousy, converges to a mechanism revealing a potential separating equilibrium. Let us point out a particularly new result when we relax the hypothesis of agents with the same risk aversion in the framework of the utility expectation model: the possibility of a competitive equilibrium with free entry and strictly positive profit.