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on Economic Design |
| By: | Frank Yang; Piotr Dworczak |
| Abstract: | Multidimensional screening is (in)famously intractable. In this paper, we study optimal screening mechanisms subject to a tractability constraint from the agent's perspective. Specifically, we require that the menu of options offered by the designer can be ordered so that, regardless of her preference type, the agent can find a utility-maximizing option via greedy search: any locally optimal choice must also be globally optimal. In one-dimensional screening with the single-crossing property, this requirement has no bite. In multidimensional environments, however, searchability restricts the set of implementable outcomes. In the multiproduct monopoly problem, the optimal searchable menu is a sparse upgrade menu: higher tiers offer higher allocation probabilities for every good, and the number of tiers is at most the number of goods. In a multidimensional screening problem with money and ordeals, the optimal searchable menu offers the agent a single way to obtain the good. In income taxation with rich multidimensional heterogeneity, a tax schedule is searchable if and only if it is progressive. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.17446 |
| By: | Michael Ostrovsky; Andrzej Skrzypacz |
| Abstract: | We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the bids or on the product of bids and deterministic quality scores. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction, although under some conditions the relation may also be reversed. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.00334 |
| By: | Federico INNOCENTI; Nicola DONI; Domenico MENICUCCI |
| Abstract: | This paper is about a two-bidder auction setting with endogenous and costly entry in which, before the bidders' entry decisions, the seller may release information about the object on sale. This information affects each bidder's belief about the own distribution of value for the object on sale, hence it affects the bidder's incentive to enter. The seller uses a second price auction and we consider the class of unrestricted information structures using the techniques of information design in which the seller sends private messages to the bidders. We characterize the optimal information structure, which optimally trades off providing rents to the bidders in favorable (to the bidders) states of the world against inducing entry of all bidders in other states of the world (in order to generate a positive auction revenue). We compare the optimal information structure with some specific information structures examined in the literature and then show that a restriction to public messages hurts the seller significantly. We also show that using a first price auction allows the seller to earn the same revenue as when a second price auction is used. We then allow the seller to use an entry fee and jointly optimize, under some restrictions, with respect to the entry fee and the information structure. In this case the seller does not need to induce entry of all bidders to earn a positive revenue, and indeed induces entry of a single bidder, who is required to pay a high entry fee, if the entry cost is not small. But if the seller can also use a reserve price, then it is optimal to (almost) fully subsidize the entry cost and use the reserve price to extract all the bidders' rents while inducing the socially optimal entry. |
| Keywords: | Procurement Auctions, First-Price Auction, Second-Price Auction, Pre-Auction Investment, Strategic Effect, Auction Ranking. |
| JEL: | D44 D82 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2026_09.rdf |
| By: | Federico Vaccari |
| Abstract: | This paper studies optimal auctions in which the allocation creates a moral hazard problem for a third-party executor. The executor chooses effort before the winner is known. In regular independent-private-values environments, the optimal mechanism is a shadow-score auction. Each bidder's virtual value is adjusted by the shadow value of relaxing the executor's incentive constraint using that bidder's allocation state. Unlike standard scoring auctions, the score is derived from a non-bidder's moral hazard constraint rather than from a preference for quality. Reserve formats miss this ranking channel, as they can adjust whether the object is sold, but cannot favor allocation states that are more useful for motivating execution effort. The paper also studies cases in which this scoring representation breaks down and the optimal mechanism becomes a constrained shadow allocation. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.29420 |
| By: | Jacob K. Goeree (School of Economics, University of New South Wales); Luke Lindsay (Department of Economics, University of Exeter); Xavier Del Pozo (Innovation Process Technology AG) |
| Abstract: | Virtually all producers, most notably airlines and electricity generators, face avoidable fixed costs that cause non-convexities in production. Standard bilateral trading institutions such as the continuous double auction produce inefficient and unstable outcomes in the presence of avoidable costs. We design a package market that allows traders to submit schedules of quantity-contingent bids. In an experiment, we compare two continuous double-auction formats to two schedule-based variants. The new mechanisms substantially outperform the continuous double auctions, both in efficiency and in preventing seller losses. Efficiency is highest when schedules can be revised in continuous time. The mechanisms that allow sellers to express non-convex costs restore efficiency in markets where bilateral trading institutions fail. |
| Keywords: | market design, experiments, package markets, avoidable costs |
| JEL: | D47 L19 |
| Date: | 2026–08–27 |
| URL: | https://d.repec.org/n?u=RePEc:exe:wpaper:2611 |
| By: | \"Ozg\"un Ekici; Sinan Ertemel; M. Bumin Yenmez |
| Abstract: | We introduce Rawlsian equity, a notion of fairness for allocating indivisible objects among agents without object-specific entitlements. Rawlsian equity requires that an object not be assigned to an agent who ranks it more highly than another agent unless the latter receives a more preferred object. We show that the set of Rawlsian equitable allocations coincides with the set of stable allocations in an auxiliary market where object priorities depend on agents' preference reports. The agent-proposing deferred acceptance algorithm computes the agent-optimal element of this set, but no Rawlsian equitable rule is strategy-proof in general. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.29080 |
| By: | Uriel Feige; Yotam Gafni |
| Abstract: | 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. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.24600 |
| By: | Thirumulanathan D |
| Abstract: | Consider the problem of designing a revenue-optimal auction mechanism when two heterogeneous items are sold to a single buyer having independent valuations over the items. The distributions of the buyer's valuation for the items are assumed to have densities that are positive, nondecreasing, and continuously differentiable on their support sets $[c_i, c_i+b_i]$ in the positive axis. I prove that the optimal mechanism is deterministic if at least one of the minimum valuations (i.e., either $c_1$ or $c_2$) is sufficiently high. I provide a method to calculate the threshold of $(c_1, c_2)$ beyond which the optimal mechanism is deterministic. I also provide a sufficient condition on the distributions of buyer's valuations for which the individual sale mechanism is optimal. I show that when $c_1$ is low and $c_2$ is high, it is optimal for the seller to sell item $2$ at the minimum valuation $c_2$, thus effectively reducing the problem to finding the optimal mechanism in the one-dimensional setting only for item $1$. I conjecture with promising preliminary results that this result can be extended to the three-item setting. Specifically, I conjecture that when $c_1$ and $c_2$ are low but $c_3$ is high, it is optimal for the seller to sell item $3$ at the minimum valuation $c_3$, thus effectively reducing the problem to finding the optimal mechanism in the two-dimensional setting for items $1$ and $2$. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22371 |
| By: | Shunya Noda; Ayano Yago |
| Abstract: | Admission systems often fill seats by applying criterion-specific rankings sequentially. We derive criterion-wise comparative statics with respect to precedence order when rankings may be arbitrarily nonaligned, and each criterion evaluates the entire admitted set through a responsive preference. For a fixed applicant set, reversing the final two blocks makes each criterion weakly prefer the outcome in which its block is later. This comparison can reverse if two blocks are followed by another criterion, even under reserve-type rankings. Under student-proposing deferred acceptance, it can also reverse with two criteria because rejection chains change the focal college's applicant set; such feedback is the only possible source of failure. In regular large markets, failures vanish for almost all colleges and, under sufficient thickness, uniformly across colleges. Under the Boston mechanism, final acceptance prevents feedback; thus the comparison holds in every finite market for fixed submitted rank-order lists and criterion-independent acceptability. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.29139 |
| By: | Zhiyuan Jia |
| Abstract: | Are simple delegation rules optimal under ambiguity? We study delegation when the principal knows the mean, but not the distribution, of the agent's private information. In a quadratic constant-bias environment, the robustly optimal randomized mechanism is a random cap: the principal draws and reveals an upper bound below which the agent chooses freely. Randomization strictly outperforms every deterministic cap by hedging against cap-specific worst-case distributions. We characterize random caps through nondecreasing and concave expected-action rules and construct the solution using a saddle-point approach. The worst-case distribution features an exponential survival function over its continuous region and an atom at the upper endpoint. Under regularity conditions, the result extends to convex-order ambiguity. When the mean is below the agent's bias, the optimal mechanism additionally requires an incentive-neutral outcome lottery. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.19846 |
| By: | Hülya Eraslan; Jeremy T. Fox; YingHua He |
| Abstract: | Ordinal mechanisms use rankings but not preference intensities. Cardinal mechanisms also elicit school utilities, allowing them to use students’ preferences over assignment lotteries. We compare probabilistic serial with four cardinal mechanisms that maximize the same welfare objective under successively stronger restrictions: capacity-only, ε-envy-free, envy-free, and a welfare-maximizing cardinal-preference pseudomarket. Because the feasible sets are nested, maximum welfare weakly falls as the restrictions tighten from capacity alone to approximate no-envy, exact no-envy, and equal budgets with common prices. We establish positive and negative results on large-market truthtelling. All 44 theorem parts in the paper are machine-checked in the Lean 4 proof assistant. We develop methods for computing cardinal-preference pseudomarket equilibria for Seattle’s 898 students and 11 schools. Using set-identified cardinal preferences from Seattle high-school choice data, we estimate that, under exact capacity, capacity-only raises mean welfare over probabilistic serial by 0.053, equivalent to shifting 5.3 percentage points of assignment probability from the average student’s worst school to the top school. Exact envy-freeness retains 79% of this gain; best-found pseudomarket equilibria yield a mean gain of 0.002. The estimates show both the value of cardinal information and the welfare cost of pseudomarket fairness restrictions. |
| JEL: | C78 I20 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35658 |
| By: | Vravosinos, Orestis; Vives, Xavier |
| Abstract: | The lattice-theoretic approach has had a significant impact in all fields of economics, being progressively incorporated into the standard toolbox. This paper presents a selective survey with an emphasis on basic tools, some important results, and applications in industrial organization, dynamic games, games of incomplete information, and mechanism design. Frontier theoretical research employing lattice-theoretic methods continues to be developed in areas such as mean-field games and information design. |
| JEL: | C62 C72 D01 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19214 |
| By: | Daisuke Hirata; Yusuke Kasuya |
| Abstract: | 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. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.27784 |
| By: | Bo Chen; Rui Gao; Jingfeng Lu; Zhewei Wang |
| Abstract: | A team-contest designer values output rather than expenditure; nonlinear conversion makes the distinction consequential. We study two non-pecuniary instruments in majority-rule contests decided by pairwise all-pay battles with private abilities: disclosing resolved outcomes and splitting the battle schedule into finer blocks. Neither changes a battle's average pivotality; each only redistributes it across histories. Under nested information structures, this redistribution makes equilibrium ability-scaled expenditure weakly more dispersed player by player without changing its mean; expected aggregate expenditure is invariant across all designs considered. The resulting convex-order comparison ranks expected total output: convex output costs favor no disclosure and coarser temporal structures, concave costs favor full disclosure and finer ones, and linear costs make both comparisons neutral. The rankings hold for finite-support and smooth continuous-type ability distributions. The mechanism extends to degree-zero component contest technologies with a unique equilibrium outcome distribution. No and full disclosure bound every admissible public garbling. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22694 |
| By: | Aloisio Araujo; Carolina Parra; Sergei Vieira |
| Abstract: | A principal screens an agent whose technology has a minimum efficient scale, so the Spence-Mirrlees condition fails along a monotone dividing curve: the locus at which every type values marginal output equally. For the class in which this curve and the relaxed solution are both strictly monotone, the optimal contract obeys a trichotomy, governed by how the two meet: a jump is impossible when they never meet, unavoidable across a flat dividing curve, a choice across a strictly increasing one. The optimum is found, not conjectured: each solution is certified as globally optimal among all implementable allocations, deterministic or random, by dualizing the family of binding constraints through an explicit weight; the certificates require neither linear primitives nor any restriction on the shape of the contract. Under mild regularity the class comprises exactly forty configurations; each is mapped to its forced shape, solved in closed form, and certified. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.19474 |
| By: | Eliaz, Kfir; Fershtman, Daniel; FRUG, ALEXANDER |
| Abstract: | We study the optimal dynamic scheduling of workers to tasks when task-completion is privately observed (hence, workers can delay the release of completed tasks), and when idle time is the only means of providing incentives. Our main result characterizes a scheduling rule, and the equilibrium it induces, maximizing the expected discounted output subject to workers' incentive constraints. When workers are inherently slow, a simple rotation scheme suffices to attain first-best output, but when they are more productive, optimal scheduling alternates between phases with and without delay. Our analysis highlights a trade-off between the quality and size of workforce. |
| JEL: | D02 D23 D73 D82 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19307 |
| By: | Rui Mao; Tingliang Huang; Houcai Shen |
| Abstract: | Artificial intelligence (AI) is increasingly integrated into medical decision-making, yet its liability implications remain complex, particularly when physicians differ in diagnostic skills and their quality is unobservable. This paper develops a principal-agent model in which a social planner designs medical liability to regulate a physician with private quality information who chooses between a standard treatment, a personalized judgment-based treatment, or following an imperfect AI recommendation. Our analysis yields several novel insights. First, we show that the optimal mechanism under asymmetric information is surprisingly simple: a uniform, one-size-fits-all liability level for all physician types who deviate from the standard of care. Despite physician heterogeneity, this simple policy often achieves the full-information first-best outcome, particularly when standard care is reliable or AI is highly accurate. Second, the relationship between AI accuracy and optimal liability is non-monotonic. Contrary to common intuition, better AI does not always imply more relaxed liability. As AI accuracy increases, the optimal liability either decreases monotonically or follows an inverted-U pattern, depending on the uncertainty of the standard treatment. Third, asymmetric information does not universally reduce social welfare. Welfare loss arises only when standard care is unreliable and AI accuracy is too low; even then, its magnitude follows an inverted U-shape, initially increasing as AI complicates the regulatory problem, but declining as more accurate AI helps mitigate it. Finally, we find that information asymmetry is a double-edged sword in the presence of AI, and greater transparency does not benefit all stakeholders equally. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03114 |
| By: | Federico Etro |
| Abstract: | We study moral hazard by managers engaged in cost-reducing activities under incentive contracts à la Holmstrom-Milgrom and monopolistic competition. Moral hazard affects both managerial incentives and market structure, generating potential paradoxes. The main one is that moral hazard can increase equilibrium effort and reduce prices by discouraging entry and expanding firm scale. Alternatively, it can foster entry by relaxing incentive contracts and reducing fixed costs of managerial compensation. We analyze equilibria under general cost and demand functions, and compare equilibrium and optimal effort and entry for CES, Logit and Linear demand systems. |
| Keywords: | Managerial compensation, moral hazard, incentive mechanisms, Holmstrom-Milgrom model |
| JEL: | L1 L4 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2026_16.rdf |