Papers

We present several models of strategic choice concerning equilibrium reasoning and behaviour, as well as new applications to dynamic games. We propose concepts such as historical equilibrium, simple Nash equilibrium, cautious backward induction, and an approach inspired by how chess players reason in sequential games.

The random-order interpretation of the Shapley value specifies both a terminal allocation and a payment path: each entrant is paid her marginal contribution at the time of entry. We embed this path in a finite dynamic entry problem in which a selected player may accept immediately or defer and allow another outsider to enter first. A flow is fully voluntary when immediate acceptance is optimal at every decision state. Although this criterion is defined through optimal continuation values, backward induction yields an equivalent system of linear inequalities in full-consent continuation values. The distinction between allocation and path is sharp in convex games: the Shapley allocation lies in the core, but the Shapley flow is fully voluntary only in additive games. Nevertheless, every efficient allocation admits a budget-balanced fully voluntary implementation when signed payments are available. We select a canonical implementation by minimizing distance from the Shapley flow, derive a reduced quadratic program for symmetric cardinality games, and study equal residual sharing, which selects the terminal allocation endogenously. With two player types, the selected allocation is an affine combination of the Shapley and equal-division allocations. Examples illustrate the effects of payment restrictions and a possible conflict between full voluntariness and coalitional stability.

We provide the first polyhedral characterization of worker-quasi-stable matchings in the classical one-to-one matching model. By modifying the classical stability constraints, we introduce a convex polytope and prove that it is integral. Consequently, its extreme points coincide exactly with the incidence vectors of worker-quasi-stable matchings, demonstrating that worker-quasi-stability preserves the geometric tractability of standard stability.

The von Neumann-Morgenstern axioms are uncontroversial desiderata for individual decision-making. We say that a bargaining solution is rational if it can be interpreted as the most preferred alternatives under these axioms. Yet, neither the Nash nor the Kalai-Smorodinsky bargaining solution is rational in this sense. We formalize two consequences of rationality, namely that one can neither be strictly better off nor strictly worse off from randomizing over different actions. These two axioms, together with other standard axioms, characterize the relative utilitarian bargaining solution. We then implement this bargaining solution in sub-game perfect equilibrium.

The axioms underlying Arrow's impossibility theorem are very restrictive in terms of what can be used when aggregating preferences. Social preferences may not depend on the menu nor on preferences over alternatives outside the menu. But context matters. So, we weaken these restrictions to allow for context to be included. The context, as we define, describes which alternatives in the menu and which preferences over alternatives outside the menu matter. We obtain unique representations. These are discussed in examples involving markets, the intertemporal well-being of an individual, and bargaining.

We ask how an expert panel should disclose auditable conflicts of interest when reports are named and experts care about their reputations for ability. Before sealed binary assessments are filed, an auditor commits to disclosing no orientation information, each named expert's orientation, or only the number of experts oriented in each direction; disclosure occurs after reports are locked. Holding reporting behaviour fixed, composition disclosure and individual attribution are exactly Blackwell-equivalent for learning the state at every finite panel size. Conditional on named reports remaining public, composition is minimal among state-lossless disclosures of orientations: every lossless public message must make the composition recoverable together with the reports. Incentives nevertheless differ sharply. In the large-panel limit near pooling, the local career returns to following evidence against one's orientation under attribution, secrecy, and composition disclosure stand in the ratio 1:4:5. On an open set of parameters, the two extreme regimes have only pooling within symmetric cutoff strategies, while composition disclosure admits a tremble-robust informative equilibrium. Near the lower boundary of this region, a sequence of composition equilibria is sparse—the evidence-following rate is of order 1/N—yet induces a nondegenerate state experiment. Anonymous disclosure can therefore preserve the information available under attribution while creating stronger incentives to produce it.

This paper studies the composition of taxation when the government cannot fully commit to respecting private returns after investment. A fiscal authority must finance a given expenditure from labor and capital income. Ordinary tax receipts are protected, but an opportunistic executive can seize part of the remaining capital payment. We show that a revenue-neutral increase in the capital tax raises the probability of compliance whenever the labor tax is below its local, fixed-wage revenue peak, provided the equilibrium remains on a regular mixing branch. This result does not depend on the elasticity of substitution between capital and labor. The same reform can raise investment: the gain in expected retention must outweigh the decline in the opportunist's continuation gain as compliance becomes less informative. We also characterize the Ramsey allocation conditional on full compliance. Limited commitment then imposes a ceiling on sustainable capital payments, rather than a general lower bound on the statutory capital-tax rate. Finally, we distinguish a change in the authority's concern for the future from an increase in both actors' patience. The former favors more informative policies when continuation welfare is convex; the latter has no unconditional direction in the reduced-form policy problem.

Local asymptotic minimax (LAM) risk is a foundational efficiency criterion in statistics and econometrics. The literature uses two definitions of LAM risk: one which appears in classical lower bounds and another which appears in arguments establishing attainment of those bounds. Conventional efficiency arguments are consistent with any estimator-dependent weighted average of the two, and consequently do not reveal which of these generalized $\alpha$-LAM risk indices describes researchers' actual preferences. We take a decision-theoretic approach to systematically resolve this ambiguity. We axiomatically characterize the set of preferences with a generalized $\alpha$-LAM representation, and we document that such preferences may violate basic rationality requirements such as Monotonicity. Motivated by this, we axiomatically characterize the subset with constant-weight representations. Within this class, a Sample Uncertainty Aversion axiom uniquely selects attainment LAM. We argue that Sample Uncertainty Aversion is normatively appealing, and we therefore recommend attainment LAM as the functional form for LAM risk.

Bernheim, Braghieri, Martínez-Marquina, and Zuckerman (2021, American Economic Review) develop a theory of chosen preferences and conjecture convergence to pure worldviews at low mindset flexibility. We show that the (original) conjecture fails: with arbitrarily many worldviews, a common-value action sustains mixed worldviews in every stationary equilibrium from a relatively open set of initial worldviews, even when all pure worldviews are absorbing. However, finite linear programs characterize a sufficient persistence condition. Conversely, mixed accumulation points require shared valuation maxima. If each implementable action has a unique maximizing evaluator, every existing stationary equilibrium converges to purity for all interior flexibility and discount parameters. Experienced utility converges without uniqueness. In existing equilibria, small payoff perturbations preserve compromise over fixed horizons with high probability. Strictly tailored worldviews yield existence and a one-step equilibrium characterization at sufficiently low mindset flexibility; weak implementation can preclude stationary pure-strategy existence. The persistence and convergence results extend to stationary randomization.

We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Characterizations are provided for deterministic signaling functions, based on simultaneous posterior matching, a constructive partition criterion, and common knowledge components. This study elaborates on the work of Blackwell (1951) in games with incomplete information, using the common knowledge components of Aumann (1976).

We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.

Moving from geographically fragmented to pooled waiting lists in deceased-donor organ transplantation can improve efficiency, but it raises concerns about regional fairness and participation incentives. This paper studies Pareto gains from such transitions in a multi-class queueing model with impatient agents, perishable items, and a tractable homogeneous compatibility friction. Unlike standard approaches that focus on static match quality or ignore regional incentives in dynamic settings, our analysis identifies dynamic risk pooling as the main source of Pareto improvements for regions: pooling reduces organ waste due to stochastic supply-demand fluctuations, temporal mismatches, and random compatibility outcomes. Although this dynamic surplus theoretically permits Pareto improvements, a purely utilitarian policy that treats all patients equally across regions often fails to deliver them when regions are asymmetric. In such cases, utilitarian redistribution extracts too many organs from high-supply regions and violates their participation constraints. To resolve this conflict, we show that the set of achievable utilities can be described by mixtures of static priority index policies. Building on this structure, we propose the Constrained Pareto Frontier Search (CPFS), a polynomial-time procedure that computes an approximately optimal allocation policy with arbitrarily small participation-constraint violations. The results suggest that, by adjusting priority indices to keep redistribution within the gains from pooled supply, demand, and compatibility risk, policymakers can attain global efficiency while preserving local participation incentives.

We study anonymous binary social choice functions on the universal weak-preference domain when the society of voters is countably infinite. Voters may strictly support one of the two alternatives or be indifferent, and non-manipulability is required in the form of coalitional strategy-proofness. Full anonymity reduces the relevant information about a coalition not to its cardinality alone, but to its cardinality signature: finite of size \(k\), infinite with infinite complement, or cofinite with complement of size \(k\). Recording the signatures of the two strict-support coalitions yields an infinite triangular grid, ordered by increasing support for one alternative and decreasing support for the other. We prove that anonymous coalition strategy-proof binary social choice functions are exactly those obtained from super order closed subsets, i.e. upper sets, of this grid. We then give a geometric classification of these subsets. Unlike in the finite-voter case, they need not be generated by their minimal elements: countable infinity creates missing-boundary regions corresponding to finite opposition or cofinite strict support. We prove an exact representation of these subsets by genuine or missing-boundary corners, and derive a nonredundant parametrization by an antichain and, when necessary, one exceptional missing-boundary region. This yields four generalized zigzag forms and completes the infinite-society counterpart of the known geometric representation for finite electorates.

This paper introduces segregation monotonicity as a criterion for evaluating measures of inequality in social networks. A network inequality measure satisfies segregation monotonicity if, holding the distribution of income fixed, it weakly increases as the network becomes more segregated according to a specified transformation of network architecture. I investigate this property using a class of level-$k$ star networks that represent increasing social segregation in the following sense: relatively poorer individuals become increasingly isolated from one another and their social comparisons become increasingly concentrated among richer individuals. I show that a relative deprivation-based measure of inequality, which aggregates comparisons with richer network neighbors, satisfies segregation monotonicity. By contrast, total experience-based measures, which aggregate absolute income differences among all network neighbors, do not generally satisfy segregation monotonicity and can decline as segregation rises. I also establish several relationships between the total experience-based measures and the standard Gini coefficient. The results show that alternative network-based inequality measures can embody fundamentally different conceptions of socially relevant comparisons.

Early-career work both signals a worker's ability and builds long-run skills. We introduce an AI industry into a career signaling model. The industry sells tokens, which workers convert into output indistinguishable from their own. We compare three regimes: no token trade, purchases only, and open trade with side sales. With no token trade, market learns every type, signalling incentives create a rat race and workers work above the full information level. With token purchases only, lower types buy output but the market still learns every type. Buying by lower types raises the signal higher types must post, so the high types can work harder than before AI. Buyers work less with AI, even below the full-information level. With side sales and abundant AI, the signal no longer depends on effort and every type under-invests in skill. Workers gain from token trade only when welfare improves, never the reverse, and the difference is the AI industry's profit. In education, where output has no value, every worker loses in the separating equilibrium, but with valuable output and cheap tokens everyone gains. Token taxes, wage taxes, and watermarking have ambiguous effects on workers' payoffs and welfare, and their effects depend on whether workers can sell output on the side.

This paper is the first work at the intersection of game theory and property testing, giving algorithms and lower bounds for efficiently testing whether an allocation mechanism is incentive compatible (IC). We propose distinguishing whether a mechanism is $\epsilon$-far from being IC, i.e., when it observes many monotonicity "violations." Conceptually, inspired by the literature on Boolean function monotonicity testing, we construct a tester for discrete single-parameter allocation rules. Technically, our work is the first to consider monotonicity testing of vector-valued functions on the hypergrid. We give a $\tilde{O}(n/\epsilon)$-query algorithm to test whether a function (representing n-player allocation mechanisms) is coordinate-wise monotone versus $\epsilon$-far from it. We also show a matching lower bound: the class of coordinate-wise monotone vector-valued functions on a Boolean hypercube or hypergrid requires $\tilde{\Omega}(n/\epsilon)$ queries to test whether it is $\epsilon$-far from monotonicity, and this holds even if the tester is two-sided and allowed to make adaptive queries. Finally, we extend our upper bound to and give a tester of the same query complexity for pricing functions of allocation mechanisms. This requires overcoming the technical challenge that the path in function space to the closest IC mechanism may involve interdependent changes to both the price and the allocation rule.

The return-on-investment (ROI) constraint is central to many auctions, particularly in online advertising, where a bidder is unwilling to pay more than a fixed fraction of the value obtained. We study truthful and revenue-maximizing auctions for ROI-constrained bidders. We first characterize truthful auctions when both valuations and ROI constraints are private, showing that the allocation rule uniquely determines the payment rule. Building on this characterization, for multiple bidders we introduce $\sigma$-increment mechanisms that resemble Myerson's optimal mechanism~\cite{journals/mor/Myerson81}; as $\sigma$ vanishes, these mechanisms become asymptotically optimal among deterministic truthful mechanisms, and their revenue approaches at least a $1/\bar r$ fraction of the optimal expected revenue over all truthful mechanisms, where $\bar r$ is the largest possible ROI constraint. In the single-bidder setting, we prove that every truthful auction can be replaced by a convex pricing function with weakly higher payments for every type, and we derive the optimal pricing functions when either the valuation or the ROI constraint is public.

An adviser who warns that a task is difficult may become harder to evaluate when her advice is followed more thoroughly. We study a long-lived adviser and successive short-lived workers who choose between standard and intensive implementation. Standard implementation reveals whether the warning was correct and gives the next worker an opportunity to acquire cost-saving practical knowledge. Intensive implementation protects the project but produces only occasional evidence about the adviser. We construct a stationary sequential equilibrium in which the adviser initially accepts an informative implementation, withholds the next project after her reputation improves, and resumes recommendations once inherited know-how has been lost. The interruption is chosen because it changes the successor's implementation decision: preserving know-how reverses the adviser's preference at the relevant history. All realized evidence remains public. Weak subsequent evidence eventually ends the low-ability adviser's protection, but this can take a long time.

We study coordination games in which every action requires planning and preparation. Before players act, they can revise their plans based on partially revealing information about their adversary's preparations. Precise information enables agents to screen for cooperation, selecting the payoff-dominant equilibrium either via small exogenous trembles or via payoff uncertainty. Across scenarios, we emphasize that decomposing an action into (i) preparation and (ii) execution allows us to analyze simultaneous-move games where players partially observe each other's contemporaneous actions.

Consider a situation wherein a decision maker sequentially searches for the best alternative among heterogeneous options with an arbitrary search order. The agent partially learns the value of an option when inspecting it. The information structure jointly determines the ex-ante and ex-post value of investigating each option, thereby shaping the entire learning path. We characterize the set of all search behaviors compatible with some information structure, which forms a polytope. A single information structure rationalizes all these search behaviors, which minimizes the agent's welfare among all information structures. Under certain symmetry assumption over primitives, we also examine the set of all feasible pairs of search and choice behaviors, with and without option sellers' price competition, and prove the same results. Our study not only provides a simple framework for analyzing how information shapes ordered learning paths, but also offers sharp insights into information design and identification problems in such environments.

The Money Pump Index (MPI) of Echenique et al. (2011) measures the severity of consumer irrationality, but computing the exact mean and median MPI over all revealed preference cycles is NP-hard (Smeulders et al., 2013). Existing solutions rely on heuristic proxies, such as evaluating only shorter cycles or bounding the MPI. By framing revealed preferences as a directed graph, this paper projects choice violations onto fundamental cycle bases, which are minimal sets of linearly independent cycles that span the graph's entire cycle space. This yields computationally tractable estimators for the mean and median MPI that are asymptotically equivalent to the original MPI. Applying this methodology to the scanner dataset analyzed by Echenique et al. (2011) and Smeulders et al., (2013), the proposed estimators compute quickly and with negligible small-sample bias.

Long-running AI agents create a control problem: each action they take changes the state, which in turn affects the trajectory of future actions. If the agent is not fully aligned, then guaranteeing safety requires approving consequential actions before allowing them to be executed. But requiring human approval at every step makes attention a bottleneck. Delegating review to other AI agents raises the same alignment problem: the reviewers may themselves be misaligned. We identify a condition on a reviewing panel that is weaker than individual alignment yet necessary and sufficient for a guarantee that the principal fares at least as well in expectation as under a designated baseline policy. Each reviewer agent reports whether an action proposal made by a proposer agent improves its own utility relative to the baseline. We show that a threshold rule tolerating $k$ disapprovals is safe exactly when, after any $k$ reviewers are removed, the principal's utility can be written as a nonnegative combination of the remaining reviewers' utilities, plus a term that is nonnegative on every feasible proposal. We call this property $k$-robust coalitional alignment. The characterization lifts to sequential control: in a discounted MDP with an arbitrary proposer agent, safety at every state is both necessary and sufficient for the induced policy to match or improve on the baseline. When reviewers vote strategically, full-panel coverage in reward-function space guarantees that every Nash equilibrium is safe under the unanimous approval rule; in contrast, more permissive thresholds can admit unsafe equilibria even when reviewers are individually aligned. Experiments with existing reviewer models show that collective review can remain sound without an aligned individual, even when some disapprovals are tolerated.

We study revenue-maximizing attention allocation on an ad-funded social media platform governed by recommendation algorithms. Attention is costly and can be monetized through advertising or allocated to increase creators' exposure, creating a trade-off between monetization and production incentives. In a two-sided model with heterogeneous viewers and creators under private information, the optimal recommendation mix includes content that is ex post suboptimal for some viewers to leverage network externalities. These distortions are targeted: low-ability creators are excluded, while high-ability creators are subsidized through exposure or monetary payments. Two-sided complementarities reshape content variety and quality, with implications for personalization regulation and advertising markets.

A principal faces a decision problem under uncertainty and can contract with a researcher to provide relevant information. The cost of acquiring information is only known to the researcher, and, moreover, by privately making an investment the researcher can reduce their expected cost. We characterize optimal contracts by reducing the problem to information design with cost constraints. The principal induces investment below a cutoff in its sunk cost. With two cost types, investment may be underprovided but is never excessive relative to the first best. With more types, the cutoff property survives but overinvestment can occur. Investment incentives also reshape information acquisition: optimal experiments may need to generate more distinct beliefs than there are possible states, and their design can be sensitive to the principal's initial beliefs.

Inferring intelligence from observable behavior is a foundational challenge in artificial intelligence. We develop a theory of Bayesian intelligence for agents such as language models. Each prompt induces a possibly imperfect internal experiment; the agent updates a full-support prior by Bayes' rule and faithfully reports its posterior over the possible answers to the question. Repetitions draw fresh, independent outcomes from the same unobserved experiment at one fixed state. We show that the agent's behavior admits this explanation if and only if its reports are not fully contradictory, i.e., some state remains possible under every report across all prompts. Report frequencies and the sizes of positive probabilities impose no further restrictions. We further propose and characterize the behavioral implications of an intelligence order that makes the behavior of two agents consistent with one agent having access to a more informative experiment: there should exist a coupling of report distributions such that the more informative agent's report excludes every answer excluded by its counterpart. Finally, we show the difficulty of aggregating coarse reports from intelligent agents: unless the agent reports a belief about the complete state of the world, the optimal aggregation can assign arbitrary weights to states that have not been excluded. These results provide a basis for understanding when agents' behavior is intelligent and highlight the difficulty of rejecting Bayesian rationality.

States and alliances spend enormous resources signaling resolve to deter adversaries. Two canonical strategies are burning money (sunk costs) and burning bridges (audience costs). Large audience costs can deter effectively, but they may be infeasible and, even when feasible, can increase the likelihood of war relative to burning money. We propose a signaling design in which the defender retains the flexibility to fight or back down but commits ex ante, before learning its resolve, to a rule mapping realized resolve into costly actions. When audience costs are limited, this design raises defender payoffs while reducing the likelihood of war. We discuss implementation through laws and automated algorithms. We also characterize defender payoffs when audience costs are chosen endogenously from a feasible set, showing that lowering the maximum feasible audience cost can raise defender payoffs, and we compare these payoffs with those under the standard burning-money setting without commitment.

Complementary resources are often allocated by agencies that see different coordinates of an individual's needs. If an intervention requires complementary resources, an agency may know if said person lacks its own resource; yet not know if supplying completes a useful bundle. We study allocation of $m$ divisible complementary goods when each agency observes only its own coordinate of a baseline-access profile. To isolate information from incentives, we measure the welfare cost of this split against a generous decentralized benchmark DEC: the best rule that acts on local information alone, with cooperative agencies and known population distribution and capacities. Even so, local observation alone can make optimally coordinated policies arbitrarily inefficient: a factor linear in $m$ (even with equal capacities), and a factor inverse in OPT (with but three agencies). Threshold referrals recover much of this loss: an agency reports if its value lies below a public threshold, and a clearing rule uses only the joint reports. Aggregating types by their reports captures a rectangle under the optimal half-utility survival curve. Our main tool is a profile-level charging certificate: if optimal utility is at least twice a threshold, OPT pays at least that on every deficient coordinate. This yields welfare at least ${\rm OPT}/[4(1+\ln(2/{\rm OPT}))]$ with one bit per agency; and an equal-revenue family shows this log-loss tight for one threshold. A geometric threshold ladder improves this to a constant fraction of OPT with doubly-logarithmic messages: a staircase recovers ${\rm OPT}/8$ with $\Theta(\log\log(1/{\rm OPT}))$ bits, and this is necessary within the class. The results isolate how a simple reporting language turns large local-info losses into constant-factor recovery. In short: One threshold gets a log-approximation. A staircase, with log-of-log bits, a constant-factor.

We introduce a notion and motivation for very credible auctions. This is a strengthening in the commitment in the credible auctions setting, making it more suitable for a modern digital applications.

Observed choice in a dynamic game mixes current profit with continuation value. A rival adds a second problem: the same comparison averages over the rival's equilibrium policy. Changing the primitive transition rewrites continuation technology; changing the rival's Markov policy, holding that law fixed, rewrites the mixture over rival-contingent payoffs. The two are not substitutes. For a rival-feature payoff of rank $K$, rank identification up to location requires $\Ephi=\lceil(MK-1)/(M-1)\rceil$ policy environments, and a second kernel when payoffs are saturated. Rank can still be restored by arbitrarily small policy differences. Independent private shocks force mixed rival actions to factor, so a payoff that depends jointly on $d$ rivals is visible only at order $\eta^{d}$ near a common interior baseline. Either rank fails or the smallest identified singular value is at most $\kappa\eta^{\dPhi}$, independently of how many kernels are stacked. Oracle-GLS variance in that direction vanishes only if $n\eta^{2\dPhi}$ diverges. An Anderson–Rubin set that carries first-stage error in the design matrix covers without a vanishing-risk condition. On U.S.\ airline entry, even among rank-identified directions, the most favorable rival-dependent contrast is several times wider than observed behavior.

We study strategy-proof social choice where agents have single-dipped preferences and outcomes may be sets of alternatives. While point-valued strategy-proof rules select an endpoint, we ask which outcomes survive when sets are compared through responsive extensions. Under the standard responsive extension, preferences over fixed-length intervals remain single-dipped, so the endpoint restriction persists and anonymity yields a single-threshold rule. Under responsive dominance, the incomplete order shared by all responsive extensions, an interior interval can survive because the two extreme intervals need not be comparable. For arbitrary sets, requiring every chosen alternative to be most preferred by some agent yields voting-by-committees rules, with one committee per endpoint; anonymous rules have a two-threshold quota form. The characterization holds on the entire endpoint-peaked domain, and every such rule is group-strategy-proof.