Papers

We study robust mechanisms when the designer possesses a Bayesian belief over some components of agents' private information but faces ambiguity over others. The designer evaluates mechanisms by their worst-case performance over all joint distributions consistent with her belief over the Bayesian components. The framework encompasses settings such as multidimensional delegation in which a principal knows the distribution of the state but not the agent's preferences (e.g., his tradeoffs across dimensions), screening in which a seller only has misspecified estimates of buyer preferences, and auction and voting design when agents' beliefs about each other are ambiguous to the designer. We provide conditions under which a knowledge-based mechanism—one that conditions only on the Bayesian components but not the ambiguous ones—is robustly optimal. Our results unify earlier work across distinct economic environments and uncover new applications.

Extending the Price-and-Choose (P&C) mechanism of Echenique and Nunez (2025), we propose the Price-Accept-and-Choose (PA&C) mechanism, which preserves efficiency while eliminating P&C's first-mover advantage. We then analyze randomized and bidding variants and show that the resulting equilibrium payoffs correspond to standard solutions in transferable utility games: the Center of the Imputation Set value for P&C and the Shapley value for PA&C. In the randomized variants, these solutions arise in expectation; in the bidding variants, they are implemented on every equilibrium path. We further relate other efficient designs, such as balanced VCG payments, to additional solution concepts, forging an interpretable bridge between implementation theory and cooperative game theory.

We study a network formation game in which agents sponsor links at a linear cost in order to maximize centrality, defined as a weighted sum of walk counts with positive and weakly decreasing weights. This class includes Katz Bonacich centrality and total communicability and captures environments in which access decays with distance. Our main result is a sharp equilibrium characterization: every Nash equilibrium network is core periphery, meaning there exists a set $C$ such that every node is linked to every node in $C$, and there are no other edges. The driving force is that linking to better connected agents generates many additional short connections at once, so incentives concentrate links on a dense subset. Finally, we show that the welfare maximizing network is always either empty or complete.

Two contestants with possibly different marginal costs compete across identical battlefields governed by a Tullock technology with discriminatory power at most one. A symmetric schedule divides a fixed prize according to the number of victories. Allowing for inactivity, unequal efforts across battlefields, and arbitrary mixed strategies, we prove the existence and uniformity of equilibrium. Equilibrium may be pure, semi-pure (one contestant mixes), or two-sided mixed; in a two-sided mixed equilibrium, each contestant uses at most countably many positive effort levels. Multiple equilibria with different structures can coexist while generating the same expected effort, prize share, cost, and payoff. For every admissible schedule and cost ratio, equilibrium is unique with six or fewer battlefields, whereas seven first permits multiplicity or two-sided mixing. We also characterize all equilibria under majority rule.

For an exogenous source of information and a prespecified number of messages k, I characterize the set of maximal–that is to say, undominated–summaries of the information that use at most k messages. When the exogenous information produces a regular distribution over posteriors (if it has a density on its affine hull, for instance), the maximal summaries take a precise geometric form. They are hierarchical power diagrams: convex subdivisions of the space of beliefs constructed by recursively subdividing cells according to weighted proximity criteria.

I show that the equivalence in finite social-choice environments of Bayesian incentive compatibility and dominant-strategy incentive compatibility holds universally if and only if every type-dependent difference in the valuation of prizes operates through a single scalar type index. Beyond binary domains this universal robustifiability is nongeneric.

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 characterise the division rules for claims problems that satisfy equal treatment of equals, bilateral consistency, composition down, and composition up. The rules are precisely the members of a one-parameter log-exponential family $\{r^\theta\}_{\theta\in[-\infty,+\infty]}$, with constrained equal awards (CEA) and constrained equal losses (CEL) as its endpoints. For finite $\theta$, $r^\theta$ is the equal-sacrifice rule in awards for $u_\theta=\log\varphi_\theta$, where \[ \varphi_\theta(x):=\frac{e^{\theta x}-1}{\theta}\quad(\theta\ne0), \qquad \varphi_0(x):=x, \] and simultaneously the equal-sacrifice rule in losses for the dual utility $u_{-\theta}$. The proportional rule is the midpoint, $\theta=0$. Continuity of the rules are not assumed but a consequence of the other axioms.

The paper explores a theoretical freemium model for the sale of information, drawing on mathematical tools used in the study of repeated zero-sum games and Bayesian persuasion. Unlike standard Bayesian persuasion models, the information seller (IS) is indifferent to the actions taken by the information buyer (IB) and is concerned solely with maximizing the revenue from selling information. Offering some information for free may increase the IB's willingness to pay for additional information. The information that the IB seeks is about the state of the world. Initially, the IB only knows the prior distribution over possible states. The IS supplies both free and paid information through signals whose state-dependent distributions determine the IB's posterior via Bayes' rule. The IB's utility is a function of the posterior. An optimal free signal is one that maximizes the IS's expected revenue from the subsequent paid signal. That revenue is equal to the IB's expected utility gain when moving from the posterior induced by the free signal to that induced by the paid signal. The paper characterizes the optimal free and paid signals and derives a formula for the maximal revenue in terms of the IB's utility function. It shows that a revenue gain for the IS from the provision of free information is accompanied by a loss to the IB. Whether free information can increase the IS's revenue depends on the form of the IB's utility function. In the two-state case, that dependence is fully characterized. In the general case, only necessary conditions are obtained. In particular, if the IB's utility function is convex, the IS can never profit from providing free information. This occurs, in particular, when the IB uses the information to solve a decision problem. By contrast, when the IB is engaged in a strategic interaction with a third party, the IS may benefit from providing free information.

This paper examines how outside options are incorporated into payoff distributions in games with coalition structures. We introduce and characterize the alpha-value, which "fully" incorporates outside options, and provide a new characterization of the Aumann-Dreze value as an allocation rule that does not incorporate outside options. We show that the chi-value (Casajus, 2009) is a component-wise convex combination of these two values and thus incorporates outside options in a discounted form.

Limited attention forces organizations to decide not only how much to discuss, but also which issues merit discussion. We study strategic communication about a multidimensional decision when a receiver can respond only along a few endogenously chosen issues. Players agree on the ideal action but prioritize different errors. In equilibrium, communicated and omitted issues must be statistically unrelated and separable according to the sender's preferences. Thus, the sender's priorities determine the agenda; the receiver's do not. Synchronized priorities raise the receiver's best equilibrium payoff but lower his worst, so he may prefer a less synchronized sender.

We develop a computational framework for Bayesian decision-making. We show that as long as no action is optimal in every state, Bayes-optimal choice is intractable. This hardness need not arise from large action, state, or signal spaces, nor from a complicated represented utility function: extracting enough information from a hard-to-interpret signal to act optimally can itself be computationally hard. We also characterize tractability across approximation notions and identify their sources of difficulty. Under the probably approximately correct criterion, sample-based Bayesian learning is tractable if and only if the signal support is bounded. Our results provide justifications for bounded rationality, costly Bayesian inference, and sample-based Bayesian learning.

In centralized school choice, a designer who announces a mechanism may deviate from it to favor some students without being detected. A mechanism is credible if it admits no such deviation. We study this credibility problem when students do not know others' reports and may observe only part of the assignment. Credibility is demanding: among common school choice mechanisms, only deferred acceptance is credible, and only when students observe enough of the assignment. We therefore rank mechanisms by their credibility. Deferred acceptance is more credible than any other stable mechanism and strictly more credible than the Boston mechanism, regardless of how much of the assignment students observe. Its ranking relative to top trading cycles and efficiency-adjusted deferred acceptance depends on disclosure: deferred acceptance is strictly more credible when students observe the entire assignment, whereas the ranking reverses when students observe only their own assignment.

We introduce a behavioral notion of domain-specific risk aversion that separates attitudes toward risk from deterministic utility: an agent is more pure risk averse in one domain than in another if, for prizes that are indifferent under certainty, he is more averse to risk in the former domain than in the latter. We develop a model that goes beyond expected utility by allowing risk attitudes to vary across domains, while preserving expected utility within each domain. The domains are subjective and need not be specified in advance; they are identified from choice behavior. We establish uniqueness of the model's parameters and provide an axiomatic characterization.

Concave consumption functions imply a marginal propensity to consume that falls with wealth. I characterize the utility functions that guarantee this property in finite-horizon optimal saving problems with stochastic discounting, returns, income, and borrowing limits. Under conditional impatience—the conditional expected discounted gross return does not exceed one—consumption functions are always concave if and only if inverse absolute prudence, $-u''/u'''$, is concave. When no conditional-impatience restriction is imposed, hyperbolic absolute risk aversion (HARA) is necessary and sufficient for uniform concavity. Thus conditional impatience permits declining marginal propensities to consume for a preference class strictly larger than HARA.

We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Csóka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy.

We study a setting in which an agent receives private information before choosing from a menu and anticipates hindsight scrutiny. Such scrutiny creates a motive for conservatism toward menu expansions. Our key axiom, conservatism, is a direct weakening of preference for flexibility: Adding an option is weakly beneficial whenever it leaves the menu's hindsight benchmark unchanged. Together with standard axioms, conservatism characterizes a scrutiny representation of preferences over menus in which the agent behaves as if she evaluates each menu by subtracting anticipated scrutiny from the material value of informed choice. Menu preference identifies a unique minimum pair of private information and scrutiny intensity, while incorporating subsequent stochastic-choice data pins down the actual pair. Applications to medical liability and corporate innovation illustrate the implications of our model for accountability design.

The VCG family and the AGV mechanism are two classical approaches to efficient implementation in the static social choice problem. In 2024, Csóka et al. showed that AGV has critical weaknesses. In contrast, the transferable-utility Guaranteed Utility Mechanism (TU-GUM) retains all the standard desirable properties of AGV while adding further ones, including collusion-proofness, because it implements efficiency in Guaranteed Utility Equilibrium. TU-GUM also applies to a more general dynamic setting with multiple extensions. Moreover, TU-GUM is a special case of an even more general and robust mechanism that combines contingent first-price tendering with the coordinated execution of dynamic stochastic multi-agent projects through a surprisingly simple rule. This paper summarizes and connects existing results from a different perspective, with some minor new observations.

An institution that cannot compel disclosure can still allocate exposure. We study two opposed advocates who select verifiable observations and a receiver who averages the selected record without correcting for selection. The institution commits exposure before the state and evidence are known; each withheld item's assigned weight expires. With commonly known pools and strictly opposed monotone preferences, all finite-game Nash equilibria produce one action and common cutoff. In large pools with a vanishing anchor, directional tail moments determine the implementing exposure share. Under common evidence laws, equal exposure implements every state. The institutional restriction matters: full within-camp reallocation induces extreme selection and, on a fixed support, eliminates state responsiveness. In a finite-state common-law benchmark, small reallocation separates disclosure cutoffs and changes implementing shares according to favorable-tail frequencies. Variation in these frequencies across states creates a positive local welfare cost even after exposure is optimized. Ex ante results bound the cost of commitment and identify information sufficient for limiting implementation. Separately, under linear payoffs, uniform item weights and continuous evidence laws on a compact state space, all Bayesian equilibria converge to the baseline outcome when advocates observe only their own samples and learn the state. Finite-pool results characterize a precision cost under common laws, balanced exposure, uniform weights and equal limiting camp sizes, and first corrections to exact risk-minimizing shares under additional regularity.

We study the properties of the cumulative offer mechanism (COM) when institutions' choice functions satisfy strong observable substitutability (strong OS). First, we show that each of the following properties of the COM characterizes strong OS: IR monotonicity, weak Maskin monotonicity, and dropping monotonicity. Dropping monotonicity is a new condition weaker than weak Maskin monotonicity, and it is interpretable as a weakening of strategy-proofness and non-bossiness. Second, we show that when choice functions are strongly OS, weak group strategy-proofness of the COM reduces to individual strategy-proofness. However, strong OS is neither necessary nor "almost necessary" for this reduction.

While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have a much smaller and often inefficient one. We show how to enlarge this set using deposits: in each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed, the only commitment required being that of the intermediary to a refund rule fixed before play begins. The mechanism sustains payoff profiles more efficient than those of the standard equilibria, without altering the underlying game and without transfers between players. We demonstrate it on the prisoner's dilemma, a congestion game, and a public goods game, all settings where cooperation cannot emerge in the standard finitely repeated version. We also apply it to a dynamic common-pool resource, suggesting that the construction extends beyond repeated stage-games.

We study random assignment of indivisible objects among a set of agents with strict preferences and outside options. When agents may rank some objects as unacceptable, we consider different notions of measuring waste of object(s) from an ex-ante perspective. The most natural one is $q$-agent-object-waste whereby both one agent and one of his acceptable objects are unassigned with at least probability $q$. On the one hand, we show that any mechanism satisfying equal treatement of almost equals (whereby any two agents with identical rankings over objects receive the same probability shares for objects they both regard acceptable), strategy-proofness and ex-post weak non-wastefulness (whereby in any assignment in the support we cannot have that both one agent and one of his acceptable objects are unassigned) must be $q$-agent-object-wasteful with $q\geq \frac{1}{6}$. On the other hand, we show that random serial dictatorship (RSD) attains the minimal bound of $\frac{1}{6}$ in this class for four agents or three objects. In addition, we consider $q$-object-wastefulness where an object remains unassigned with probability $q$, while agents, who consider it acceptable, remain unassigned with aggregate probability $q$. We again show that RSD attains the minimal bound of $\frac{1}{4}$ in this class of mechanisms with respect to $q$-object-wastefulness for three objects. Finally, we show that random deferred acceptance (RDA) may be strictly less agent-object-wasteful than RSD (but at the cost of violating equal treatment of almost equals).

Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. For normalized binary goods, we give a polynomial-time algorithm for computing an EF1+EQ1 allocation with at most seven agents, but also construct a normalized instance with a larger number of agents for which no such allocation exists. In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante and ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.

In a number of large, important families of finite games, not only is the set of pure-strategy Nash equilibria nonempty but it is also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-reply strategy. This weak acyclicity property is weaker than acyclicity of the game, which requires every such sequence to reach an equilibrium. For example, all perfect-information extensive-form games are weakly acyclic, but they are generally not acyclic as even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to acyclicity of some priority rule, which is a rule that allows only some improvement moves. It is also equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above.

Agnostic sequential equilibrium (ASE) is a refinement of sequential equilibrium that does not force on the players a single, arbitrary belief system. In addition, whereas sequential equilibrium assumes the players' beliefs to be fully consistent (a notion that is based on perturbations of strategies), ASE employs a novel, simpler and local concept of strong consistency between strategy profiles and off-equilibrium beliefs, which is applicable to a large class of dynamic games, including games with a continuum of actions. In the last respect, the new solution concept is similar to perfect Bayesian equilibrium. It is shown that a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE precisely when it is a sequential equilibrium with every fully consistent belief system. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players' actions in some information sets partially or completely unspecified.

Generative AI relocates the fixed cost of automation. A model provider pays to train a frontier system, while a downstream firm rents capability by usage; the same firm must carry a continuing payroll to supply a human-augmented service. We study this asymmetry in a local service economy with household budgets and a market-clearing wage. Human augmentation earns a larger surplus from an additional customer, whereas automation has the lower break-even scale. Payroll supports demand across sectors. Wage adjustment works against this feedback but does not generally undo it: when the wage-income effect dominates the fall in the wage bill per retained worker, production modes are strategic complements. The economy can then possess both a high-demand human-augmented equilibrium and a low-demand automated equilibrium. The former is the local first best, even when flexible wages prevent a firm-profit ranking. With forward-looking firms and staggered revision opportunities, the same inherited employment structure can support an automation cascade or an augmentation recovery; the anticipated path of later adopters validates the first movers' choices. Under the regularity and boundary conditions of Frankel and Pauzner, a public aggregate shock selects a unique state-contingent path, while the vanishing-friction limit selects according to risk dominance. A transparent parameterization anchored to professional-services revenue-to-payroll ratios illustrates how high-autonomy uses can enter the coordination region and how wage adjustment compresses that region. Optimal policy combines the adoption wedge created by demand spillovers with a temporary bridge when the low state is locally self-sustaining.

We develop a theory of measurement scales for utility functions, based on a generalization of the notion of numeraire commodity. Every sufficiently well-behaved utility is denominated in some scale of this form, and conversely, the choice of a compatible scale unit uniquely identifies utilities up to an additive constant. We define a profile of utilities to be interpersonally comparable precisely when they are denominated in a common measurement unit. We study when profiles of comparable utilities exist, as well as how a planner ought to aggregate them, and provide applications to social choice and welfare economics.

Comparing economic models requires balancing fit against flexibility. Yet standard selection criteria often proxy flexibility using parameter counts, overlooking differences due to functional form and experimental design. This paper introduces a data compression approach for evaluating economic models. Following the Minimum Description Length principle, models are interpreted as codes and evaluated by how effectively they compress data. This perspective yields compression-based analogues of Selten's predictive success and Fudenberg et al.'s completeness and restrictiveness. Unlike Selten's measure, its analogue unifies deterministic and stochastic models in a likelihood framework; unlike Fudenberg et al.'s measures, the proposed framework provides a complete selection criterion. Applications to social preferences, risky choice, and intertemporal choice illustrate the relevance of the approach. In simulations, accounting for flexibility differences due to functional form and experimental design improves model recovery relative to AIC, BIC, and cross-validation. In empirical reanalyses, MDL changes model rankings in favor of more parsimonious specifications.

Can altruism serve as the behavioral foundation for efficient institutional design? We study full implementation in Berge equilibrium, the solution concept that formalizes strategic altruism: each agent's opponents collectively maximize her payoff. While Berge equilibrium resolves the Prisoner's Dilemma and can eliminate cooperation failures in social dilemmas, we show that this optimism does not survive the move from individual behavior to institutional design. First, we show that the weak Pareto optimal rule is not implementable in Berge equilibrium. Second, on the unrestricted domain of strict preferences, any social choice rule that is both weakly Pareto efficient and implementable in Berge equilibrium must be dictatorial. Finally, we show that Berge implementability is strictly more demanding than Nash implementability: every social goal achievable under strategic altruism is also achievable under self-interest, but not vice versa. The very feature that makes Berge equilibrium appealing at the behavioral level, that is, opponents protecting each agent's payoff, is precisely what forecloses efficient, non-dictatorial institutions at the design level.

We consider fair allocation of indivisible goods in a setting in which agents have subjective valuation functions over the set of goods, and in addition, goods may be sold at given market prices. In this setting, a fair allocation involves {deciding which goods to sell, how to allocate the unsold goods, and how to divide the money received from the sold goods.} We adapt to this setting the definitions of share-based fairness notions, such as the maximin share (MMS) and the truncated proportional share (TPS), and comparison-based fairness notions such as EF1 and EFX (which we adapt to SEF1 and SEFX). We show the following results when the utility of each agent is additive both over goods and over money. With two agents, there are allocations that are simultaneously MMS and SEFX. With three agents, there are instances in which no allocation gives every agent more than $\frac{11}{12}$-MMS. With any number of agents, there are $\frac{2}{3}$-MMS allocations. There also are allocations that are simultaneously SEFX and $\frac{n}{2n-1}$-TPS. This latter ratio is best possible, even without the SEFX requirement.