We develop a framework for mechanism design with AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure—capabilities can be concealed but not counterfeited—yields a revelation principle, a characterization of implementable policies via nested cyclical monotonicity, and conditions under which eliciting higher-order beliefs can discipline multiple agents. We apply our framework to stylized examples of (i) sandbagging in which a more capable agent pretends to be less capable; (ii) an alignment–interpretability trade-off, where the two are substitutes in the instrument but complements in value; (iii) discipline via peer scoring; (iv) coupling rewards to induce competition among multiple agents; and (v) scalable oversight and reward shaping.

We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profits. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level as a by-product of reducing the information rents of the buyer.

We develop an integrated framework for information design and mechanism design in screening environments with quasilinear utility. Using the tools of majorization theory and quantile functions, we show that both information design and mechanism design problems reduce to maximizing linear functionals subject to majorization constraints. For mechanism design, the designer chooses allocations weakly majorized by the exogenous inventory. For information design, the designer chooses information structures that are majorized by the prior distribution. When the designer can choose both the mechanism and the information structure simultaneously, then the joint optimization problem becomes bilinear with two majorization constraints. We show that pooling of values and associated allocations is always optimal in this case. Our approach unifies classic results in auction theory and screening, extends them to information design settings, and provides new insights into the welfare effects of jointly optimizing allocation and information.

How should a buyer design procurement mechanisms when suppliers' costs are unknown, and the buyer does not have a prior belief? We demonstrate that simple mechanisms - that share a constant fraction of the buyer utility with the seller - allow the buyer to realize a guaranteed positive fraction of the efficient social surplus across all possible costs. Moreover, a judicious choice of the share based on the known demand maximizes the surplus ratio guarantee that can be attained across all possible (arbitrarily complex and nonlinear) mechanisms and cost functions. Similar results hold in related nonlinear pricing and optimal regulation problems.

We study the role of information in Bertrand competition with differentiated goods and heterogeneous production costs. When producers know their costs and consumers know their values, consumer surplus and total surplus are aligned, in the sense that the information and equilibrium that maximize consumer surplus also maximize total surplus. Alignment may fail if consumers do not know their values: Partial information about values makes purchases less efficient but intensifies price competition. We illustrate this within a Hotelling duopoly framework. (JEL D11, D43, D82, D83)

Consider an analyst who models a strategic situation using an incomplete information game. The true game may involve correlated, duplicated belief hierarchies, but the analyst lacks knowledge of the correlation structure and can only approximate each belief hierarchy. To make predictions in this setting, the analyst uses belief-invariant Bayes correlated equilibria (BIBCE) and seeks to determine which one is justifiable. We address this question by introducing the notion of robustness: a BIBCE is robust if, for every nearby incomplete information game, there exists a BIBCE close to it. Our main result provides a sufficient condition for robustness using a generalized potential function. In a supermodular potential game, a robust BIBCE is a Bayes Nash equilibrium, whereas this need not hold in other classes of games.

We formalize Tilly’s concept of repertoires of collective action and analyze how state repression affects the variety of observed contentious actions. When repression accelerates with higher levels of antiregime actions (convex repression structure), opposition leaders tend to call for many different forms of contentious actions, thereby generating a wider repertoire. In contrast, when repression decelerates with higher contentious actions (concave repression structure, including indiscriminate repression), opposition leaders tend to call for just one form of contentious action, thereby generating a narrower repertoire. Methodologically, we deliver an analysis for settings in which coordination and delegation are intertwined. (JEL D71, D72, D74, D82)

Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology" reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. An information structure is said to be simple if each player has a finite set of types and each type has a distinct first-order belief about payoff states. We show that simple information structures are dense in the almost common knowledge topology and thus it is without loss to restrict attention to simple information structures in information design problems.

What outcomes can be implemented by the choice of an information structure in binary‐action supermodular games? An outcome is partially implementable if it satisfies obedience (Bergemann and Morris (2016)). We characterize when an outcome is smallest equilibrium implementable (induced by the smallest equilibrium). Smallest equilibrium implementation requires a stronger sequential obedience condition: there is a stochastic ordering of players under which players are prepared to switch to the high action even if they think only those before them will switch. We then characterize the optimal outcome induced by an information designer who prefers the high action to be played, but anticipates that the worst (hence smallest) equilibrium will be played. In a potential game, under convexity assumptions on the potential and the designer's objective, it is optimal to choose an outcome where actions are perfectly coordinated (all players choose the same action), with the high action profile played on the largest event where that action profile maximizes the average potential.

We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.

We consider the problem of a leader who can assign rewards for citizens for different anti-regime actions. Citizens face a coordination problem in which each citizen has a private, endogenous degree of optimism about the likelihood of regime change. Because more optimistic citizens are easier to motivate, the choice of optimal rewards entails optimal screening. This leads to a distribution of anti-regime actions. A key result is the emergence of a vanguard, consisting of citizens who engage in the endogenous, maximum level of action. Other citizens participate at varying degrees, with less optimistic citizens contributing less. We explore how the regime's strength or the maximum reward available to the leader influences the distribution of actions. Moreover, we show that more heterogeneity (e.g., higher inequality) among potential revolutionaries reduces the likelihood of regime change. Our methodological contribution is that we deliver a sharp and novel marriage of screening and global games.

The arrival of digital commerce has lead to an increasing use of personalization and differentiation strategies. With differentiated products along the quality dimension and/or the quantity dimension comes the need for nonlinear pricing policies or second degree price discrimination. The optimal pricing strategies for quality and quantity differentiated products were first investigated by Mussa and Rosen (1978) and Maskin and Riley (1984), respectively. The optimal pricing strategies were shown to depend heavily on the prior distribution of the private information regarding the types, and ultimately the willingness-to-pay of the buyers. Yet, frequently the sellers possess only weak and incomplete information about the distribution of demand. This paper aims to develop robust pricing policies that are independent of specific demand distributions and provide revenue guarantees across all possible distributions.

We characterize global game selections in binary-action supermodular games in terms of sequential obedience: it is shown that an action profile of a binary-action supermodular game is a (possibly noise-dependent) global game selection if and only if it satisfies strict sequential obedience and strict reverse sequential obedience.

We study a strict version of the notion of equilibrium robustness by Kajii and Morris (Econometrica 65:1283–1309, 1997) that allows for a larger class of incomplete information perturbations of a given complete information game, where with high probability, players believe that their payoffs are close to (but may be different from) those of the complete information game. We show that a strict monotone potential maximizer of a complete information game is strictly robust if either the game or the associated strict monotone potential is supermodular, and that the converse also holds in all binary-action supermodular games.

The zero lower bound causes bias in the estimation of linear models. A common solution seen throughout the literature is to utilize nonlinear models instead. But if said bias were analytically tractable, one could also retain linear frameworks, and apply a correction. I show this is true for workhorse linear Gaussian structural vector autoregressions.

This note demonstrates how the insights from Morris et al. (2020) can be applied to the problem of optimal joint design of information and transfers in team production.

For binary-action supermodular games with a continuum of symmetric players, we show that simple global game information structures can be used to implement an optimal outcome under adversarial equilibrium selection.

We study a coordination game where players choose what information to acquire about payoffs prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional defined on information structures. A cost functional satisfies continuous choice if players choose a continuous decision rule even in a decision problem with discontinuous payoffs. If continuous choice holds, there is a unique equilibrium; if it fails, there are multiple equilibria. We show how continuous choice captures the idea that it is sufficiently harder to distinguish states that are close to each other relative to far away states.

We characterize the revenue-maximizing information structure in the second-price auction. The seller faces a trade-off: more information improves the efficiency of the allocation but creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition is high) but to pool high values (where competition is low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising. (JEL D44, D82, D83, M37)

We describe a methodology for making counterfactual predictions in settings where the information held by strategic agents and the distribution of payoff-relevant states of the world are unknown. The analyst observes behavior assumed to be rationalized by a Bayesian model, in which agents maximize expected utility, given partial and differential information about the state. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of the state and agents' information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, the counterfactual prediction is described by finitely many linear inequalities, even though the latent parameter, the information structure, is infinite dimensional. (JEL D44, D82, D83)