This thesis consists of three independent chapters.
– A decision-maker must accept or reject a privately informed agent. The agent always wants to be accepted, while the decision-maker wants to accept only a subset of types. The decision-maker has access to a set of feasible tests and, prior to making a decision, requires the agent to choose a test from a menu. I show that the DM does not benefit from commitment in this context. I then show in various environments when the DM benefits from offering a menu. When the domain of feasible tests contains a most informative test, I characterise when only the dominant test is offered and when a dominated test is part of the optimal menu. I also consider settings where types are multidimensional or where tests vary in difficulty.
– I consider a model of monopoly pricing where a firm makes a price offer to a buyer with reference-dependent preferences. The reference point is the ex-ante probability of trade and the buyer exhibits an attachment effect: the higher his expectations to buy, the higher his willingness-to-pay. When the buyer’s valuation is private information, a unique equilibrium exists where the firm plays a mixed strategy and its profits are the same as in the reference-independent benchmark. The equilibrium always entails inefficiencies: the probability of no trade is greater than zero. Finally, I show that when the firm can design a test about the buyer’s valuation, it is better off using a noisy test.
– I provide a sufficient condition under which a principal does not benefit from commitment in economic situations described by a constrained maximisation problem. Commitment has no value when the textit{marginal} contribution of the constraints is null in the problem with commitment. I use this result to extend multiple results in mechanism design.