Nathan Hancart

In many situations, decision-makers depend on tests to inform their choices. I consider a decision-maker that has access to a set of feasible tests and, prior to making a decision, requires a privately informed agent to choose a test from a menu. By offering a menu, the decision-maker can use the agent's choice as an additional source of information. The decision-maker must accept or reject the agent. The agent always wants to be accepted, while the decision-maker wants to accept only a subset of types. First, I show that the decision-maker does not benefit from commitment in this context. I use this result to show in several economic environments when the decision-maker benefits from offering a choice of test. When the domain of feasible tests contains a most informative test, I give necessary and sufficient conditions for when only the dominant test is offered for any prior and when a dominated test is always part of the optimal menu. I also show when the decision-maker benefits from a menu when types are multidimensional or tests vary in their difficulty.

I consider a model of monopoly pricing where a firm makes a price offer to a buyer with reference-dependent preferences without being able to commit to it. 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: even as the firm's information converges to complete information, it mixes on a non-vanishing support and 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 can do strictly better than in the reference-independent benchmark by leveraging the uncertainty generated by a noisy test.

I provide a sufficient condition under which a principal does not benefit from committing to a mechanism in economic models represented by a maximisation problem under constraints. These problems include mechanism design, principal-agent models or sender-receiver games. In principal-agent problems, this condition holds if the agent has a finite strategy space and the principal's value function is continuous in the mechanism.

Two identical firms compete to attract and hire from a pool of candidates of unknown productivity. Firms simultaneously post a selection procedure which consists of a test and an acceptance probability for each test outcome. After observing the firms' selection procedures, each candidate can apply to one of them. Both firms have access to a limited set of feasible tests. The firms face two key considerations when choosing their selection procedure: the statistical properties of their test and the selection into the procedure by the candidates. I identify two partial orders on tests that are useful to characterise the equilibrium of this game: the test's accuracy (Lehmann, 1988) and difficulty. I show that in any symmetric equilibrium, the test chosen must be maximal in the accuracy order and minimal in the difficulty order. Intuitively, competition leads to maximal but misguided learning: firms end up having precise knowledge that is not payoff relevant. I also consider the cases where firms face capacity constraints, have the possibility of making a wage offer and existence of asymmetric equilibria where one firm is more selective than another.