Theoretical Economics Papers

ALT When allocating indivisible goods, the maximum Nash welfare rule is known to be the unique welfarist rule satisfying envy-freeness up to one good. We strengthen this characterization by showing that envy-freeness up to one good can be replaced by substantially weaker fairness requirements: envy-freeness up to k goods or proportionality up to k goods, for any fixed k. Our characterization holds even for profiles with identical goods.

ALT We introduce a mediator to a communication setting with verifiable (hard) evidence and characterize precisely when mediation can induce every obedient outcome–every type-contingent distribution of actions that the receiver is willing to follow–including the outcome that delivers the sender's commitment (Bayesian persuasion) payoff. For both type-independent and general preferences, it is necessary for each type to have a message he alone can send. This is also sufficient for type-independent preferences, whereas the general case also requires a particular alignment of the types' utilities. We also rank evidence structures by the distributions of actions conditional on the sender's type that they can induce at (mediated) equilibrium, through garbling conditions analogous to Blackwell's comparison of experiments.

ALT I study the optimality of selling K heterogeneous objects to a buyer with private values through a quantity menu: the seller posts a price for each number of objects, and the buyer chooses a quantity, pays its price, and selects any objects up to that quantity. I propose a pricing method that aggregates critical values for second differences of quantity values (the highest values attainable at each quantity). Critical values can be determined separately when each second difference's conditional inverse-hazard ratio depends only on that difference. For additive values, I show that the resulting menu is optimal among all incentive-compatible and individually rational mechanisms under explicit distributional and support conditions, including ex ante symmetry across object labels. A separate result applies the same pricing method to obtain an optimal menu for nonadditive bundle values without ex ante symmetry, assuming free disposal, independence between the quantity-value vector and the v

ALT Variation in grading standards across instructors who teach the same students is evidence of a moral hazard problem, whether or not grades are inflated. The optimal standard is the same for every section of a course, yet grades vary widely across sections. We present a principal-agent model in which instructors who know the optimal standard still depart from it, leniently or harshly, depending on their incentives. Penalizing deviations from the department average leaves the average unchanged but compresses grading variance, which raises student welfare. Disclosing the same information to students instead increases grading variance.

ALT We study the steady states of games played recurrently within large anonymous populations of players who receive partial ex-post feedback about the play of their opponents. Departing from the classical Bayesian account, players do not trust their conjectures as a correct description of the strategic environment but consider them as approximations of a reality that is only partially modeled and partially observed. We introduce games with feedback and uncertainty attitudes, in which the normal-form structure is enriched with a profile of feedback functions and, for each player, a preference functional that encodes aversion to misspecification and to ambiguity. The induced misspecification sensitive criterion contains the variational, maxmin, and smooth-ambiguity evaluations as special cases and collapses to expected utility when beliefs are unambiguous and the player is neutral to misspecification. The appropriate steady-state notion for such games is the Self-Confirming Equilibrium unde

ALT We study sharp bounds on equilibrium behavior in Bayesian games when players may make mistakes. Under strategic complementarities, the set of behavioral perfect equilibria has a largest and a smallest element, both in pure strategies. We ask when these bounds are monotone and how they depend on the way mistakes are made. For monotone supermodular games, we consider limits of equilibria under increasing perturbations, in the sense that conditional tremble distributions have full support and increase stochastically with type. We show that the largest and smallest perfect equilibria exist, which are pure and monotone. Under the general perfection notion, the extremal perfect equilibria continue to be monotone in the setting with finite actions. With infinite actions, the extremal perfect equilibria can be nonmonotone, and the set of perfect monotone equilibria can even lack extrema.

ALT Convexity of preferences is a pervasive assumption in economic analysis, so it is important to understand how this property is revealed in data. In this paper, we develop a method to test for convexity given partial preference information in the form of weak and strict incomplete orders. We characterize the pairs that can be extended to convex preferences and provide an efficient algorithm to verify this property. Requiring the convex preference to align with an order that satisfies independence, such as the Euclidean order or stochastic dominance, does not complicate the test. We apply our results to consumer demand, choice under risk and uncertainty, and preferences over information, and establish conditions under which upper semicontinuity or continuity can also be obtained. We identify environments in which convexity imposes no additional restrictions beyond rationality, extending Afriat-type results to infinite data and co-convex budgets and establishing a convex version of exact

ALT This paper revisits the consumer search and price competition model of Wolinsky (1986). Suppose that the market has a finite number of firms, and the match value distribution function and survival function are both log-concave. Then, there is a unique symmetric pure-strategy equilibrium price with active consumer search. Two applications are discussed.

ALT Generative AI can lower the cost of producing polished application materials without improving applicants' abilities to do the job. We study an employer who observes qualifications and work history, summarized by observable quality, but must infer other job-relevant attributes from reports that applicants can manipulate at costs that depend on privately known manipulation ability. The employer commits to a hiring rule under a capacity constraint, and we evaluate rules by match value net of applicants' manipulation costs. We show that, as manipulation ability becomes increasingly dispersed among applicants with the same observable quality, socially optimal hiring converges to selection on observable quality alone, a phenomenon we call strategic feature collapse. To capture the remaining welfare gain from reports, we construct a simple dual-track mechanism that directly admits applicants with high observable quality and offers some otherwise excluded applicants a report-based route to ad

ALT Sustaining efficient trade under private information requires external subsidies. Although a designer cannot avoid deficits on average, they can control exposure. We characterize efficient and truthful mechanisms that minimize the worst-case deficit in markets with many buyers and sellers, under interim participation. This problem is dual to maximizing expected trade surplus under correlation ambiguity, with constraints on submarkets with one agent removed. In bilateral trade, the best deficit ceiling is the competitive surplus in a benchmark continuum market, achieved by a "competitive pivot mechanism". In larger markets, optimal mechanisms are characterized in terms of worst-case residual welfare contributions, but solutions exhibit a complex combinatorial structure. We obtain explicit guarantees under natural participation charge restrictions and establish how the best deficit excess decays as market thickens. Our duality characterization is general and extends to many mechanism des

ALT In a market in which any coalition can reach agreements, a stable outcome need not exist even when agents have substitutable preferences. We show how regulation can restore stability. If a regulator participates in every agreement, a setwise stable outcome exists when each ordinary agent's preference satisfies a condition weaker than substitutability, while the regulator's preference remains largely unrestricted. An alternative existence result allows ordinary agents to have arbitrary preferences while requiring the regulator to support each agent's profitable contract deletions. Our results apply to matching markets involving regulated activities.

ALT We study consensus formation and information acquisition in conferences where DeGroot-type opinion updating is constrained by an acceptance rule based on Kullback-Leibler divergence. Players choose private information experiments before deliberation, and these choices determine both their posterior distributions and acceptance tolerances. We establish sufficient conditions for global consensus under specified conference structures, including repeated bilateral conferences organized by a fully receptive mediator. Under full reimbursement of the mediator's conference costs, the information-acquisition game has a weighted potential and admits a pure-strategy Nash equilibrium. We develop a numerical procedure using verified payoff bounds over the continuous posterior domain to certify approximate equilibria and assess partial reimbursement policies that preserve a given equilibrium profile. The binary state, three-player examples illustrate how conference order interacts with state varianc

ALT A long-lived sender repeatedly advises a myopic receiver who observes only the recommendation record. Nonbinding, observable self-restraint, such as a rolling quota on favorable recommendations, makes each favorable recommendation use capacity that could serve future opportunities, inducing selective advice. With two actions, when obedience requires a strictly positive cost of self-restraint, the sender's normalized equilibrium payoff is subject to a ceiling equal to the payoff from the best credible partitional signal minus the expected cost of self-restraint. This bound holds at every discount factor; under an upper-tail condition, rolling quotas approach it as the sender becomes patient. A sufficiently valuable opportunity can also induce an informative violation that ends communication.

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.