We study the optimal design of tests with manipulable inputs. Tests take a unidimensional state of the world as input and output, an informative signal to guide a receiver's approve or reject decision. The receiver wishes to only approve states that comply with her baseline standard. An agent with a preference for approval can covertly falsify the state of the world at a cost. We characterize receiver‐optimal tests and show they rely on productive falsification by compliant states. They work by setting a more stringent operational standard, and granting noncompliant states a positive approval probability to deter them from falsifying to the standard. We also study how falsification‐detection technologies improve optimal tests. They allow the designer to build an implicit cost of falsification into the test, in the form of signal devaluations. Exploiting this channel requires enriching the signal space.

This paper makes a first attempt at building a theory of interim Bayesian persuasion. I work in a minimalist model where a low or high type sender seeks validation from a receiver who is willing to validate high types exclusively. After learning her type, the sender chooses a complete conditional information structure for the receiver from a possibly restricted feasible set. I suggest a solution to this game that takes into account the signaling potential of the sender's choice.

We study selection rules: voting procedures used by committees to choose whether to place an issue on their agenda.At the selection stage of the model, committee members are uncertain about their final preferences.They only have some private information about these preferences.We show that voters become more conservative when the selection rule itself becomes more conservative.The decision rule has the opposite effect.We compare these voting procedures to the designation of an agenda setter among the committee, and to a utilitarian social planner with all the ex interim private information.

We provide the first analysis of altruism in networks. Agents are connected through a fixed, weighted network and care about the well-being of their network neigh-bors. Given some initial distribution of incomes, agents may provide financial support to their poorer friends. We characterize the Nash equilibria of this transfer game for general networks and utility functions. We show that equilibria solve a well-behaved maximization program, related to classical problems of optimal transportation on networks. We build on this reformulation and establish existence, uniqueness in consumptions and generic uniqueness in transfers. We show that transfers are affected by the geometry of the altru-istic network. They flow through shortest paths and chains of transfers emerge when the network is not transitive. We analyze the effects of changes in incomes and in the network. When an agent suffers a negative income shock, the equilibrium consumption of every agent decreases weakly. We characterize the impact of small redistributions and show that decreasing income inequality may increase consumption inequality. We also characterize the impact of a small increase in altruism. While altruistic networks reduce inequality, more altruism may lead to more inequality.

This article asks when communication with certifiable information leads to complete information revelation. We consider Bayesian games augmented by a pre-play communication phase in which announcements are made publicly. We first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). Next, we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure. This characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in games with strategic complementarities, voting with deliberation, and persuasion games with multidimensional types.