Nathan Hancart

We study cheap talk with simple language, where the sender communicates using a score that aggregates a multidimensional state. Both the sender and the receiver share the same payoffs, given by a quadratic loss function. We show that the restriction to scores introduces strategic considerations. First, equilibrium payoffs can be strictly lower than those achievable under commitment to a scoring rule. Second, we prove that any equilibrium score must be either linear or discrete. Finally, assuming normally distributed states, we fully characterize the set of equilibrium linear scores, which includes both the ex-ante best and the worst linear scores.

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.