We develop a verification theorem for infinite-horizon optimal stopping under G-Brownian motion and apply it to several stopping problems of economic interest. The theorem gives sufficient conditions under which a candidate solution to a system of variational inequalities is the value function under volatility, covariance, or joint drift–volatility ambiguity. In the canonical irreversible investment problem, volatility ambiguity advances investment because the worst-case scenario selects the lowest feasible volatility for a convex continuation value. Ambiguity about volatility therefore acts in the opposite direction from volatility itself, which postpones investment. In other environments, worst-case volatility can vary with the state, alter project relevance, create bilateral valuation wedges, shorten search, and change two-dimensional investment payoffs through covariance and correlation ambiguity. A common convexity-based mechanism drives these results: volatility ambiguity changes the perceived dispersion of future outcomes, whereas drift ambiguity acts through monotonicity.
Complexity aversion in choice under risk is well documented. One of its main behavioral effects is the event-splitting effect. It captures how the value of a lottery changes when one prize is split into two prizes, each with half the original probability. We weaken independence and continuity to accommodate the event-splitting effect. The resulting preferences admit either an expected utility representation with an additive entropy cost of complexity or a power-weighted expected utility representation in which probabilities are weighted by a power function. The model also provides behavioral foundations for logit choice.
Despite addressing similar underlying questions, the literatures on network formation and matching have evolved more or less independently. This paper offers a common framework, studying a general model of network formation without externalities-equivalently, a one-sided many-to-many matching model. I give conditions for the existence and uniqueness of stable graphs, I prove a rural hospital theorem, and I highlight a link-by-link conflict of interest across different stable graphs. Special cases contain and extend classic results for the roommate problem and two-sided matching markets. An iterated deletion algorithm adapted from Gutin et al. (2023) furnishes a crucial tool, reducing network formation games to a normal form with helpful properties.
We propose a mean-field game (MFG) approach to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking intertemporal utility-maximizing agents work and migrate in a two-dimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of a circular economy, we obtain closed-form solutions for small perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior.
We enrich standard models of imperfect competition by allowing consumer demand for market goods to depend non-separably on off-market time. Consumers value final consumption experiences that require both market purchases and time, which reshapes demand elasticities through two opposing forces. First, because time is an input, changes in market prices translate only partially into changes in the cost of an experience and second, households can substitute time for market purchases in response to price variation. We show how these forces alter the mapping from markups to welfare by distinguishing between markups and a holistic counterpart that accounts for the time cost of consumption. In a monopolistically competitive environment with CES preferences over experiences, firm selection and entry is governed solely by the elasticity of substitution between time use and market purchases, and markup dispersion can be consistent with efficiency when time and market purchases are perfect complements. Extending the analysis to oligopolistic competition, we show that forces that raise markups, like greater market concentration and less competitive conduct, also amplify the gap between the usual and holistic markups.
The Taylor principle, a more than one-for-one reaction of the nominal interest rate to inflation, is a central tenet of monetary policy to rule out self-fulfilling equilibria. The standard sticky-price model only holds this principle as a sufficient determinacy bound, with substitutes such as output-gap targeting available. We show that if the long-run Phillips curve is vertical, the Taylor principle is necessary and no amount of output-gap, output-growth, or forecast targeting can substitute for the vigorous response to inflation it prescribes. Sticky price models report determinacy bounds as generically model-dependent, nonlinear functions of model parameters. We find that models with vertical long-run Phillips curves share the same determinacy bounds despite differing short-run tradeoffs. These bounds are more conservative, placing tighter restrictions on monetary policy, and more robust, being independent of model-specific parameters and depending solely on monetary policy’s reaction to current inflation.
We show in a model of RFQ trading that customers may admit only a few dealers, even when more are available, to induce maximum liquidity supply—“less can be more.” The number of admitted dealers is pinned down by a competition elasticity, shaped by dealers’ cost to respond to RFQs. For example, higher search (operating) costs increase (reduce) admitted dealers. A social planner would mandate even fewer dealers than the market outcome, because customers induce excessive dealer competition. The model predicts endogenous market power, yields implications for regulation and design of electronic platforms, and speaks to customer-dealer interactions under market stress.
We examine optimal strategy-proof voting mechanisms in environments where the designer lacks precise information about the probability distribution of individual utility profiles. This uncertainty over the true distribution is represented by a set of multiple distributions, and the designer evaluates mechanisms using either the worst-case utility sum or worst-case regret. Departing from the existing literature, we do not assume that utility functions are single-peaked or that the set of possible utility functions is maximally rich. In this setting, we show that the median voter rule is the unique optimal mechanism under both criteria. Our result provides a new justification for this well-known mechanism from a welfare perspective.
Given a model of preferences, what choice data or experiment is sufficient to definitively test whether a subject is consistent with the model or to classify them into some "type" within the model? We characterize all experiments that test or classify a given model using a novel graph-theoretic construction: the labeled permutohedron. We show how these results can be used to identify the smallest experiments that achieve a particular goal.
A Hard Problem is a collective choice problem in which the only feasible alternatives to the status quo consist of a welfare gain to some people (the Winners) and a welfare loss to others (the Losers). These problems are typical in a number of settings, such as climate action, anti-trust regulation, and tax design. We study how to make collective choices when faced with Hard Problems. We find that a relatively weak fairness requirement, which we call Expansion Solidarity, necessarily leads to a dictatorship of the Losers, no matter how small their number. Even one single Loser must be given the power to veto any departure from the status quo, regardless of the number of Winners, how large the gains, how small the loss, or how extreme the welfare inequalities.
In this paper, we characterize a forecasting model where forecasters cannot perfectly distinguish between the two persistent components (trends and cycles) in a dynamic setting. In this model, forecasters jointly update their beliefs about the two components: noisy information about one component is used to update beliefs about the other component. We present diagnostic empirical facts on forecasting behaviors and show that these facts are consistent with our model's predictions while contradicting those of existing models in the expectation formation literature. To validate our model, we exploit the Federal Reserve's 2012 adoption of explicit inflation targeting as a policy shock. Structural estimation reveals that this policy change altered the underlying data generation process, and the corresponding changes in forecasting behavior indeed align with our model's predictions. Finally, we revisit the standard Forecast Error-Forecast Revision regression approach in this literature. We examine its robustness within our enriched framework and reveal that trend-cycle confusion can interact with behavioral bias and generate horizon-dependent overreaction patterns documented in empirical studies.
The paper studies the canonical hold-up problem with one-sided investment by the buyer and full bargaining power by the seller. The buyer can covertly choose any distribution of valuations at a cost and privately observes her valuation. I show that, unlike in the well-understood case with linear costs, if investment costs are strictly convex, the buyer's equilibrium utility is strictly positive and total welfare is strictly higher than when valuations are public information, thus alleviating the severity of the hold-up problem. In fact, when costs are mean-based or display decreasing risk, the equilibrium outcome might be efficient.
We study pseudonymity—an information regime where agents’ histories are perfectly observable, but linked only to pseudonyms rather than to true identities. A key feature is that agents may open and use multiple pseudonyms simultaneously. In a tractable environment with limited commitment, we characterize the set of stationary credit equilibria under pseudonymity, showing that it forms a strict non-empty subset of equilibria attainable under a no anonymity regime, where histories are publicly linked to true identities. Moreover, money is always essential under pseudonymity, yet cannot co-exist with credit. Finally, imposing optimal fees on pseudonym creation generally raises welfare, whereas making pseudonyms tradable never does.
We show that a temporary tightening of unsecured credit limits can raise welfare in competitive economies with limited commitment. When default excludes agents from borrowing but not saving, the value of default becomes price-dependent. Because agents do not internalize the effects of borrowing limits on equilibrium prices and participation constraints, laissez-faire limits need not be welfare-maximizing. A pre-announced, transitory tightening raises bond prices (lowers interest rates), reduces the value of default, and relaxes self-enforcing borrowing limits in earlier periods. If the resulting expansion of risk sharing outweighs the temporary distortion when the cap binds, the policy delivers an ex ante Pareto improvement. The mechanism has a natural macroprudential interpretation, implying, under certain conditions, that reneging cannot be supported by unanimity once the policy is announced, and can also deliver welfare gains even in the absence of output penalties, low interest rates, and bubbly debt limits.
In the standard dynamic screening problem between an uninformed seller and a privately informed buyer, theory suggests that the presence (absence) of the buyer’s outside option leads to a substantial surplus for the seller (buyer). This outcome arises from contrasting unraveling processes that theory predicts: negative selection occurs in the absence of an outside option, while positive selection occurs in the presence of it. We examine the validity of these contrasting unraveling processes and report laboratory data that qualitatively deviate from theoretical predictions. We found that the seller’s profit ranking was reversed between the two environments. In particular, in the presence of an outside option, the buyer frequently rejected current-round offers, leading to pervasive delays; and the seller’s reported beliefs about the buyer’s type were qualitatively more consistent with the negative selection than with the theoretically predicted positive selection.
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders have substitutes preferences for the goods. We then develop a theory of complementarities specifically tailored to assignment stages of spectrum auctions. Assignment stages typically guarantee contiguous spectrum to each winner—this proves to be an especially severe joint feasibility constraint. We propose a definition of bidder complementarities and further dichotomize them as direct or indirect. When opponents bid on distinct parts of a bidder’s preferred assignment, they set up a direct bidder complementarity. However, if an assignment is denied through the contiguity restriction, that is called an indirect complementarity. As a result, non-core outcomes, together with all of the accompanying anomalies, can be expected in VCG assignment stages. We then examine a conspicuous recent spectrum auction, the FCC’s Broadcast Incentive Auction, and we provide the first documentation of zero-revenue outcomes in the field. Of 207 assignment stage auctions with at least three bidders, 17.9% produced non-core outcomes relative to the bids and, of these, 3 generated zero revenues. After rescaling bidder values, we find that the majority of assignment stage auctions had the potential for exploitable bidder complementarities and that the vast majority of bidder complementarities—both potential and realized—were indirect.
We study a persuasion problem in which the receiver has the ability to probabilistically verify the state at a cost. The sender wants to convince the receiver to accept a project, but the receiver is only willing to accept the project when its quality is above a threshold. The optimal disclosure policy strikes a balance between influencing the receiver’s decisions to accept and to verify the quality. It is deterministic and involves at most three messages, each consisting of an acceptance recommendation and a verification recommendation. Under the optimal disclosure policy, the acceptance recommendation exhibits a cutoff structure, while the verification recommendation exhibits a negative assortative structure. Specifically, the optimal disclosure policy recommends acceptance when the quality exceeds a certain threshold. When the quality falls below this threshold, rejection without verification is recommended. For qualities above the threshold, verification is not recommended if the quality lies within the middle range of the interval. Using the characterization of the optimal disclosure policy, we conduct comparative statics and show that verification is recommended when the probability of successful verification is moderate.
Perfect equilibrium and its refinements are widely studied and typically rely on full-support perturbations. We introduce a S-localized notion of perfection for games with a continuum of players. It confines perturbations within a S-neighborhood of the underlying action distribution and eliminates undesirable equilibria from a local perspective. We establish the existence of a pure strategy S-localized perfect equilibrium and show that it is equivalent to S-admissible Nash equilibrium. We also study limit versions of S-localized perfection. Illustrative applications to large routing games and crowd saturation games are presented.
