ALT We formulate the design of a market stability reserve as a stationary mean-field singular control problem. The allowance balance follows a regime-switching diffusion, while the regulator injects or withdraws allowances through bounded-variation controls. The objective trades off the average allowance balance, its stationary dispersion, deviations from a long-run target, and intervention costs. The optimal policy is a regime-dependent band rule characterized by four reflecting thresholds. Its computation reduces to a scalar fixed-point problem combining a coupled variational inequality with the invariant distribution of the reflected process. A calibration to the EU ETS yields thresholds of the same order of magnitude as the existing Market Stability Reserve rule. Comparative statics show that volatility is the main determinant of the intervention band, whereas the frequency and duration of crisis regimes have limited effects. A simpler two-threshold policy based on average regime dynam

ALT In this paper, we identify level-k reasoning in repeated games that operates at the level of a supergame strategy. First, we develop a model of level-k reasoning that incorporates choices over strategies as well as beliefs about the strategies chosen by others. Then, jointly using elicited strategies and beliefs about strategies from the indefinitely repeated Prisoner's Dilemma, and applying a new notion of balance-optimal error tolerance, we classify a substantial fraction of subjects as level-1 or level-2. Moreover, we show that when level-k reasoning operates at the level of a repeated-game strategy, cognitive ability and experience predict higher level reasoning.

ALT The existing literature on monetary-fiscal policy interactions emphasizes that an active monetary/passive fiscal policy regime causes global indeterminacy of equilibrium, supporting liquidity traps and self-fulfilling hyperinflations as possible equilibrium outcomes. In a nonlinear New Keynesian model with costly price adjustment, I show that an analogous critique, with different global macroeconomic dynamics, extends to a passive monetary/active fiscal policy regime whenever the fiscal response to government liabilities is below the steady-state real interest rate but positive. In this case, although the equilibrium is locally unique according to the Blanchard-Kahn conditions, there exist multiple inflation paths originating around the saddle path that converge asymptotically to the central bank's target rate while satisfying the private sector's transversality condition. I demonstrate that global determinacy instead requires a pure regime of fiscal dominance, with primary surpluses s

ALT We develop a framework for assessing implementation impossibilities through the information required to resolve them. Domain covers describe information used to select a mechanism without restricting admissible preferences. Coarsening a cover weakens the required information. In quasi-linear public decision problems with a status quo, we study two impossibilities of dominant-strategy implementation: combining efficiency and individual rationality with either budget feasibility or budget balancedness. Under an interval cover based on bounds on maximal social surplus, we characterize the social choice rules implementable in dominant strategies and satisfying the first set of axioms. Under a surplus-level cover based on exact surplus levels, we obtain the corresponding characterization for the second set of axioms. Both covers are minimal: no strictly coarser cover permits implementation under the respective requirements. These economically interpretable minimal covers deepen our understa

ALT Large language model (LLM) platforms introducing advertising must decide how much capability ad revenue should fund and what consumers should pay to avoid ads. We study a monopolistic platform that jointly chooses costly response quality, advertising intensity, and subscription prices when advertising reduces user value but better service raises advertising returns. Three findings follow. First, when partly ad-supported and ad-free plans coexist, advertising can finance useful service for consumers who receive none under pure subscription. Lower effective quality in middle plans weakens the alternatives available to premium users, allowing higher prices for unchanged ad-free service. Some fully ad-supported users gain utility, while partly ad-supported and ad-free users lose: broader access can coexist with utility polarization. Second, an intermediate advertising cap can maximize consumer surplus by preserving some revenue that finances service while limiting degradation. Third, cheap

ALT We consider the classic bargaining problem: two players have to agree on a `fair' division (x,y) ∈ Ω⊂ ℝ≥₀² which results in Player 1 receiving x and Player 2 receiving y. The usual approach to this problem has been to impose a number of desirable axioms that a fair division should have and then conclude that the solution is uniquely defined by the axioms. We take an orthogonal view, avoid the discussion of axioms, and ask whether different and contradicting axioms may give rise to similar solutions. To this end, we define a natural metric on the space of solutions to the bargaining problem. The metric shows a strong internal consistency between the three celebrated solutions due to Nash (1950), Raiffa (1953) and Kalai-Smorodinsky (1975). It identifies problematic cases for the Utilitarian solution and the Perles-Maschler solution (1981). The area monotonic solution of Anbarci-Bigelow (1988) is shown to be nearly perfectly located on a shortest path from Nash to Kalai-Smorodinsky.

ALT We consider the Ramsey problem of optimal government policy and give examples where lotteries are essential for the optimal solution. When markets are complete and the representative agent's coefficient of relative prudence is bounded, lotteries are typically not optimal. For the incomplete markets case, we prove analytically that lotteries improve welfare for some calibrations with CRRA utility, and we give a simple numerical example for this claim. When the agent's coefficient of relative risk aversion is unbounded for small consumption, lotteries typically improve welfare and can be used to approximate the first-best solution arbitrarily well in both the complete and the incomplete markets cases. However, in the complete markets case, when debt constraints are not too tight and the representative agent is sufficiently patient, lotteries can be purified in the sense that there is a deterministic solution that gives the same value.

ALT We study dynamic test design under the threat of manipulation. At each instant, a principal who cannot commit to future actions chooses whether to hire an agent, fire him, or continue costly probation by designing a test. The test provides information about the agent's persistent type, which is either good or bad. After observing the test choice, the bad type can exert costly effort to manipulate the evidence and mimic the good type. Deterring manipulation imposes an endogenous information budget that limits how intensively the principal can test. We show that, except at beliefs that remain unchanged in the absence of news, equilibrium tests are one-sided: they generate only passes, which trigger hiring, or only failures, which trigger firing. Equilibrium outcomes feature either correct hiring and firing decisions after costly delay or immediate decisions that risk misallocation. With commitment, the principal instead keeps the test constant throughout probation, even when she is nearl

ALT We study stationary equilibrium and comparative statics in an incomplete market economy with risk-sensitive preferences. We prove that a stationary equilibrium exists for every nonnegative degree of risk sensitivity. With independent income, greater risk sensitivity weakly raises aggregate saving at fixed prices and weakly lowers the smallest and the largest equilibrium interest rates. With stochastically monotone Markov income, these comparisons hold when the lower risk-sensitivity parameter is sufficiently small or the upper parameter sufficiently large. For pairs of intermediate values, however, greater risk sensitivity can lower saving, contrary to an existing result in the literature, and can raise the smallest and largest equilibrium rates. An exact decomposition identifies the forces driving these reversals.

ALT We study the sale of an asset to competitive buyers. Before the sale, the seller can buy hard information about the asset from an intermediary who designs and prices a test to maximize his revenue guarantee across equilibria. The test consists of one or more signals, and the seller privately chooses which subset of signals to buy and selectively discloses their realization to the buyers. We show that the intermediary benefits from splitting information into multiple signals and characterize his maximal revenue guarantee as the cumulative entropy of the asset value distribution. This guarantee is achieved by a sequence of “skim from the top” tests with binary, i.i.d. signals and additive pricing. Furthermore, any sequence of tests that achieves the maximal guarantee reveals the asset's value in the limit. For binary values, we also characterize the revenue guarantee for any given number of signals, and show that it is achieved by a test that corresponds to a “Swiss cheese" model of fail

ALT Bergemann, Brooks, and Morris (2015) characterize the consumer and producer surplus pairs that segmentation can produce when the distribution of values is known. I fix only the set of possible values and characterize the pairs that some market and some segmentation can produce. They form a convex polygon. Its outer edge is the largest efficient surplus a market can have when its uniform-price profit is capped, net of that profit, and truncated equal-revenue markets attain it. At the values no segmentation is needed; strictly between two values, reaching the frontier requires splitting a market into two extremal markets. With a continuum of values up to v̄, consumer surplus is at most πln(v̄/π) when producer surplus (the seller's profit) is π, this bound is reached without segmentation, and no market gives consumers more than v̄/e.

ALT We propose a publisher content marketplace that allocates payments for information used in AI-generated answers. The unit of attribution is a “lego block:” a distinct fact or piece of commentary that may appear in articles from multiple publishers. A simple news-reading model connects three payment rules: equal sharing among all publishers reporting on a block, rewarding the publisher who reported a block first, and rewarding indispensable contributions. Each can be represented within a Shapley-value framework. We evaluate the framework using answers to 1,974 search-engine queries about a heavily covered news episode. When attribution considers only the articles retrieved for an individual query, most cited blocks appear unique, and the rules produce nearly identical allocations. A global index covering the full news corpus reveals overlap across publishers, making the choice of payment rule consequential. Premium publishers, defined as established outlets with substantial newsgatherin

ALT We study persuasion that works through memory: a manipulator alters the probabilities with which a Bayesian decision-maker recalls the signals he has received. The decision-maker corrects for the elevated or reduced probabilities of recalling different signals, and this correction disciplines what manipulation can achieve. Manipulation cannot move the average posterior. It backfires on decision-makers with few memories, whose sparse recall is evidence against the favored state, yet it is effective on those with many, who can be led to arbitrarily confident beliefs in the wrong state. It thickens the right tail of the belief distribution and, under Poisson memory, lowers its hazard rate. In a monopoly pricing application, the seller manipulates memory retrieval at high prices, and manipulation in turn raises the optimal price. In a narrative persuasion application, memory manipulation reduces information provision and creates echo chambers.

ALT In auction design with limited information about bidders' value distributions, we provide an optimality foundation for dominant-strategy mechanisms. We show that simple dominant-strategy incentive compatible (DIC) mechanisms–either a second-price auction with a random reserve or the standard second-price auction without a reserve–achieve a revenue guarantee equal to the worst-case optimal revenue attainable by Bayesian incentive compatible (BIC) mechanisms, thereby establishing a robust form of DIC-BIC equivalence.

ALT Organizations rely on languages that imperfectly represent underlying states. We study the interaction of a lying cost, increasing in the distance from the message prescribed by the language, and a deception cost, increasing in the distortion induced in beliefs. Higher lying costs reduce bias and informativeness; higher deception costs do the opposite. Full revelation is sustained as lying costs become small, but with unbounded bias and communication costs. The most efficient policies sustaining nearly full revelation feature high deception costs with some tolerance for lying. With complementarities, targeting messages both untruthful and deceptive sustains full revelation without communication costs.

ALT We study whether a planner can favor students at schools they rank more highly while preserving truthful reporting. The standard implementation of the deferred acceptance (DA) algorithm is typically not the solution. With interior cutoffs, DA with multiple tie-breaking (DA-MTB) solves the planner's optimization problem if and only if the planner's payoff from a school assignment is independent of the students' preferences. This is typically not the case, and strict incentive compatibility under DA-MTB leaves room for improvement via preference-dependent priority adjustments. We characterize optimal rank-dependent cutoff adjustments in a two-school model and show that, in a many-school environment, near-optimal approximately incentive-compatible assignments can be chosen with small support (so each type of student may only attend a small number of schools).

ALT We study matching markets with overlapping reserves governed by heterogeneous priorities. When applicants qualify for multiple reserves, how they are routed can affect reserve utilization and which applicants are admitted. We introduce classify-and-rank choice rules that yield strategy-proof deferred acceptance mechanisms satisfying maximum reserve utilization and priority-respect. We axiomatically characterize our mechanism's admission outcomes for any given classification and reserve order. With two reserve categories, we provide a foundation for the reserve order and establish its distributional implications for access across eligibility groups. Using nine cycles of Chilean school admissions, which feature such reserves, we document reserve-utilization failures under the deployed mechanism and show that their frequency depends sharply on the reserve order. We show how our mechanism can be adapted to Chile's institutional setting to prevent such failures. Under this alternative mecha

ALT This paper establishes the existence and essential uniqueness of an intuitively refined Markov-perfect equilibrium in a duopoly game with sunk costs, barriers to entry, firm-specific technological progress, and irreversible exit. We develop an algorithm that quickly computes the equilibrium by solving for fixed points of a finite sequence of auxiliary contraction mappings, which we label Fake Backward Induction. We illustrate the game's practical value with a quantitative analysis of competition policy in a stochastically growing market with firms idiosyncratically learning by aging. Computing one equilibrium of this example takes 10.2 seconds on one Apple M5 Pro core.

ALT Multiplicative Kantian equilibrium requires agents to evaluate whether they would prefer all players to change their actions by a common proportional factor. This note argues that such a counterfactual is not fully specified by the material payoff environment alone: one must also specify the scale in which proportional universalization is performed. Building on the Sher-Roemer discussion of strategic non-invariance, we characterize how a smooth monotone reparametrization of actions changes the multiplicative Kantian first-order condition. We then illustrate the issue in a simple two-country abatement problem. Universalizing physical abatement and universalizing abatement expenditures are both natural interpretations of "doing one's part," but they lead to different Kantian outcomes, even though they describe the same material environment. The note also identifies special cases in which the interior first-order condition is representation-invariant, including common-exponent power trans

ALT CEO compensation has often been examined from the top down, i.e., as the outcome of a negotiation between the CEO, the board of directors, and the shareholders. While these approaches have provided valuable insights into the nature of CEO compensation and its relations with firm performance and intra-firm inequality, we believe they leave aside the internal decision-making dynamics of CEOs and employees. To fill this research gap, we develop an agent-based model built on the NK framework in which a CEO compensated for long-term firm performance interacts with several employees rewarded for short-term departmental performance. This temporal dichotomy in their respective compensation functions creates a potential temporal misalignment of incentives. By varying the horizon considered by the CEO to make their decisions, we examine how this temporal (mis)alignment of incentives shapes firm performance and pay inequality between the CEO and the employees. Our findings suggest that aligning t