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on Microeconomics |
| By: | Andreas Kleiner |
| Abstract: | We study a model of delegation in which a principal takes a multidimensional action and an agent has private information about a multidimensional state. We provide necessary and sufficient conditions for an arbitrary mechanism to maximize the principal’s expected payoff. A key step shows that a function is the indirect utility of an incentive-compatible mechanism if and only if it is convex and lies below the agent’s full-discretion payoff. We apply our optimality conditions to convex delegation sets and characterize when a single budget optimally links decisions. Linking can preserve discretion even when separate dele gation would eliminate it. Optimal linking can also require a nonconvex delegation set, even with uniformly distributed types. If the principal cares little about aligned decisions, every optimal mechanism randomizes: risk in an aligned decision provides incentives in the biased ones at little cost to her. |
| Keywords: | delegation; mechanism design without transfers |
| JEL: | D82 D86 C61 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_784 |
| By: | Robin Ng; Greg Taylor |
| Abstract: | We study how content moderation facilitates communication on online platforms. A sender transmits information to a receiver, exerting effort to signal their truthfulness. Communication fails without moderation because the effort required is prohibitive. Moderation resolves this problem by making effort a more powerful signal of veracity. However, moderation crowds out sender effort, decreasing engagement value of content on the platform. A socially optimal policy may therefore involve limited moderation, but platforms often have an incentive to allow too much false content. We study the interaction between moderation and other strategic platform choices, including a platform’s decision to share revenue with creators, the decision to be a content-hosting platform, and the enablement of AI features. |
| Keywords: | user-generated content, content moderation, creator economy, media platforms, misinformation |
| JEL: | D83 L82 L86 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_698v4 |
| By: | Agustin G. Bonifacio |
| Abstract: | We study social welfare rules with strict individual and social preferences. A preference profile is dictatorial for a rule if the social preference coincides with some agent's preference and no agent with a different preference can change the social preference unilaterally. We establish that (i) a rule is dictatorial if and only if all of its profiles are dictatorial; and (ii) if a rule satisfies unanimity and independence (of irrelevant alternatives), then all its profiles must be dictatorial. These results constitute a proof of Arrow's Impossibility Theorem. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11851 |
| By: | Dihan Zou |
| Abstract: | We study monopoly regulation when capacity is contractible but subsequent output is not. A firm privately observes its production cost before installing costly capacity and then choosing output, while the regulator cannot use transfers. We provide sufficient conditions under which a single capacity floor implements an optimal mechanism with full participation. The floor raises output by changing investment while leaving utilization to the firm after installation costs are sunk. Under additional conditions, the allocation has three regions: laissez-faire, full utilization of the floor, and underutilization. High-cost types knowingly install capacity they will not fully use, yet produce more than under laissez-faire. This physical waste is a necessary evil of optimal regulation that expands service. We also show that underutilization can persist in optimal regulation with capacity-contingent subsidies or a common entry fee. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.07189 |
| By: | Bhavook Bhardwaj; Marco LiCalzi |
| Abstract: | We consider a model of collective choice where for each menu there is an agent who is accountable for the choice made. Specifically, we assume that two agents (individuals or selves) allocate choice tasks over different menus using an ownership rule: the owner of the decision over a menu picks what maximizes his own preference and is accountable for it. We characterize three distinct ownership rules under different (nested) choice environments. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06428 |
| By: | Guoqiang Tian |
| Abstract: | This paper develops a general framework for dynamic mechanism and information design with AI agents, encompassing optimal contracting and integrating evolving hidden information and hidden action with partial verification, technological authorization, and multi-agent interaction. It nests conventional dynamic screening, hidden-action contracting, and conditional dynamic information design, while allowing reporting, action, and information-use decisions to interact through a common continuation mechanism. We establish a dynamic revelation principle and a recursive characterization of implementability in which truthful reporting and post-report obedience are jointly determined through continuation incentives. In quasilinear optimal-contracting environments, dynamic envelope and integral-monotonicity methods yield a verification-adjusted dynamic virtual-surplus representation and identify three distinct margins: dynamic information rents, verification rents, and the implementation cost of hidden action. These margins generate a branched hierarchy separating conventional dynamic screening, hidden-action contracting, and their joint problem. We also study the joint design of monitoring, information use, and incentives: more informative monitoring capacity expands the designer's opportunity set, but full disclosure need not be optimal, and information use can itself alter hidden-action incentives. With multiple agents, correlated information, peer discipline, coupled incentives, joint feasibility, and continuation opportunities create additional strategic interactions. Although motivated by AI-agent environments, the framework applies more broadly to dynamic agency settings with similar economic features. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11177 |
| By: | Ratna K. Shrestha (University of British Columbia); Gaurav Subedi (RALP Technologies); Ayush Shrestha (Global Relay Communications Inc) |
| Abstract: | Standard theories trace information asymmetry to privately held information, heterogeneous signals, or costly information acquisition. We identify a distinct mechanism: otherwise identical rational agents observing a common Markov state at asynchronous times can hold different predictive distributions because their information differs in age. When the transition kernel separates information ages, independent Bernoulli observation arrivals make such divergence recur infinitely often almost surely, even with identical arrival probabilities. When agents instead choose costly updating intensities, independent update realizations can regenerate heterogeneous information ages among ex ante identical agents. In a stationary Gaussian AR(1) environment, the consequences depend on common staleness as well as the age gap: holding the gap fixed, older information raises individual uncertainty while reducing expected squared forecast disagreement and the value of certifying relative freshness. This generates stale consensus: low disagreement despite high uncertainty. With multiple ordered ages, costly certification supports partial-unraveling equilibria in which fresher types certify and sufficiently stale types pool. Under geometric information ages, more frequent updating weakly lowers the smallest and largest equilibrium disclosure cutoffs wherever positive-certification equilibria exist. The framework has implications for credit, insurance, financial markets, and multi-agent AI. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11200 |
| By: | Gaetano Alfredo Minerva |
| Abstract: | I propose a mechanism for the coexistence of vertical integration and outsourcing within an industry. In a monopolistically competitive model with incomplete contracts, final-good producers under either organizational form combine labor and differentiated inputs to produce fixed capital. Since its unit cost depends on the industry price index, distinct zero-profit conditions can hold, sustaining a mixed free-entry equilibrium. The forms differ in fixed-capital cost per unit of contribution to the price index; this ranking determines comparative statics and whether local stability is possible. I derive a sufficient condition ensuring stability whenever the mixed equilibrium exists. In numerical parameterizations using empirically standard elasticities of substitution, the condition holds throughout the admissible range of vertical-linkage intensity. Within the stable region, larger markets raise the integrated share without changing output prices or supplier bargaining terms. Relative firm size depends on governance costs and upstream bargaining share, so the model imposes no uniform ranking. |
| JEL: | C62 D23 D43 F12 L23 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:bol:bodewp:wp1233 |
| By: | Yuta Nakamura; Noriaki Okamoto |
| Abstract: | A second-price auction must determine its price but need not learn how far losing values lie below it. We show that protecting this information from the seller conflicts with auction credibility. In deterministic protocols with private communication, lower-tail privacy forces the first informative question to reveal whether a bidder has the highest possible value. The seller can then manipulate the winner's payment without any bidder detecting the deviation, increasing revenue at some valuation profiles and never reducing it. A descending protocol conceals losing values below the price but permits manipulation; with mandatory sale, a credible ascending protocol reveals them. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12204 |
| By: | Benjamin Marsh |
| Abstract: | A single auction can have both a shill-proof equilibrium and a non-shill-proof equilibrium in the model of Komo, Kominers, and Roughgarden. We give an explicit single item example with three bidder positions, publicly observed actions, positive winning prices, and a strictly regular i.i.d.\ value distribution. Real bidders have strict incentives in both equilibria. An initial public action conveys information about whether the final position is real. The resulting belief changes the middle bidder's response and reverses the first shill's strict preference between two actions. We verify both equilibria and compute their expected revenues. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06262 |
| By: | Galit Ashkenazi-Golan; Edward Plumb; Clemens Possnig; Yufei Zhang |
| Abstract: | We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11675 |
| By: | Federico Fioravanti; Zoi Terzopoulou |
| Abstract: | When voters evaluate alternatives sequentially, an anchoring bias makes their ballots depend on the order in which alternatives are presented. For approval ballots, no non-constant voting rule is robust to this dependence. We show that ranked ballots change the picture sharply: a rank-based rule is robust to the presentation order if and only if it is tops-only. Robustness to anchoring is thus available, but only at the price of ignoring everything a voter reports beyond her favourite alternative. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10316 |
| By: | Lijian Lu; Ce Zhang |
| Abstract: | When auction bidders misperceive their rivals, a seller can change not only the amount of information rent but also the states in which it is delivered. We ask when this payment-design opportunity survives a finite bidding interface, nonnegative-payment restrictions, and comparison with conventional auctions under the same beliefs. We formulate payment design as a linear program in nonnegative bidder rents. A single state can safely carry a report's rent when it is both cheapest for its intended type and least attractive to potential mimics. We characterize this alignment, bound the cost of a restricted payment architecture when alignment is imperfect, and use shadow prices when the rankings conflict. Own-type projection yields a unique optimal expected-payment rule for a fixed allocation. Contiguous bid bands implement truthful reporting at every value, but create pooling losses and within-band surplus. Under a separate smooth-belief model, feasible truthful rules and revenue upper bounds support comparisons with a first-price equilibrium under the same beliefs. A calibration using 1, 000 eBay proof-set auction records illustrates a partition-dependent reversal: first price dominates all exactly truthful, no-subsidy rules on ten equal-probability bands in one scenario, while a richer contingent rule on ten equal-dollar bands outperforms it. An operator should choose interface resolution, payment dependence, and integrity tolerances jointly. Validate the probabilities that support incentives, compare formats under the same beliefs, and distinguish redesign from deployment. Any receipt advantage must cover implementation costs before it can imply a profit advantage. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05650 |
| By: | Ujjwal Kumar |
| Abstract: | A planner wants to elicit partial information about a subject's preference relation. Preferences are grouped into ``types" relevant to the planner's purpose. Can the planner identify the subject's type through menu-choice data or experiment, without distinguishing preferences within the same type? We provide a complete answer by characterizing identifiable type spaces. The characterization uses a novel geometric condition, called face consistency, which governs distinctions within and across square and hexagonal faces of the permutohedron. For every identifiable type space, we explicitly construct the unique irreducible identifying experiment from its boundary. This experiment is optimal among all identifying experiments under any cost criterion for which adding menus cannot reduce cost. Using the equivalence between identifiability and elicitation with acts, as shown in Azrieli et al. (2021), we study symmetric policies requesting unranked shortlists that contain only acceptable products, include every product preferred to a selected one, and are nonempty whenever an acceptable product exists. Only two such policies are elicitable with acts: requesting the favorite acceptable product or the entire acceptable set. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10207 |
| By: | David J. Jin |
| Abstract: | An agent learns from data that many parameters of her model explain equally well. Berk's theorem states that her belief concentrates on the parameters that best fit the data, but does not select between them. We show that, with a continuum of parameters, the posterior concentrates on the best-fitting parameters with the smallest local learning coefficient. We propose a definition of narratives, subsets of the best-fitting parameters on which the learning coefficient is constant. Narratives are characterized by the number of coincidences they require (complexity) and how exactly each must hold (robustness). When the agent's actions affect her data, every long-run action is a singular equilibrium, a best reply to a belief supported on the least complex and most robust narratives. Singular equilibrium refines Berk-Nash and self-confirming equilibrium by restricting overly complex or knife-edge off-path beliefs, and its strict uniform version characterizes uniformly stable actions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11615 |
| By: | Ram Sewak Dubey; Giorgio Laguzzi |
| Abstract: | We study the existence of real-valued social welfare functions (SWFs) on the set of infinite utility streams that satisfy anonymity and almost weak Pareto. We characterize the domains of one-period utilities, \(Y\subset \mathbb{R}\), for which such SWFs exist. We show that an SWF satisfying these two axioms exists if and only if \(Y\) contains no subset that is order-isomorphic to the set of negative and positive integers. Thus, the restrictions on \(Y\) required for the existence of an SWF satisfying anonymity and almost weak Pareto coincide with those required for an SWF satisfying anonymity and weak Pareto. Moreover, the SWF we construct is invariant under arbitrary permutations and satisfies stationarity, two properties that are particularly useful for decision making in infinite-horizon economies. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05253 |
| By: | Joshua S. Gans |
| Abstract: | An advertiser in a second-price auction sees what it paid, not the rival bids that supposedly set the price. Akbarpour and Li (2020) show that an auctioneer can therefore charge a winner up to its bid undetected. The Federal Trade Commission alleges that Amazon’s advertising auctions, described as second-price, used soft reserves that did this. We ask whether repeated bidding exposes such charges and what adjustment does to welfare. If each charge equal to the bid is flagged, the soft reserve is exposed quickly, however much the advertiser trusted the description. If reports show only win rates and expected charges, it is indistinguishable from a second-price auction at any fixed bid: an advertiser that trusts the description and bids its value never learns, and one that doubts it but bids for current profit needs a number of auctions at least inversely proportional to its doubt before it considers a soft reserve more likely than not. The second-price description and aggregate reporting are complements. Among informed, symmetric advertisers, the soft reserve raises no more revenue than a second-price auction, and when only some advertisers adjust, placements are misallocated. Disclosure returns surplus to advertisers; removing the surcharge also restores efficiency. |
| JEL: | D44 D83 L86 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35841 |
| By: | Endre Cs\'oka; M\'at\'e Viczi\'an |
| Abstract: | The Guaranteed Utility Mechanism (GUM) was introduced to implement efficiency in Guaranteed Utility Equilibrium (GUE) in dynamic social choice problems. We show that this mechanism also has a previously unknown connection to risk minimization. Fixing an efficient decision policy, we study variance-minimizing budget-balanced transfer rules in the class of GUE-implementations of truthful reporting. A symmetrized version of GUM (sym-GUM) minimizes the sum of the agents' utility variances under truthful reporting when there is no public state. When a public state is present, a slight modification of this rule yields the minimizer for the same objective. Sym-GUM, however, does not minimize transfer risk. The minimizer for that problem is instead the symmetrized version of a closely related GUM-like transfer rule. In both problems, the minimizing truthful total transfers are unique up to agent-specific constants summing to zero and events of probability zero. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10456 |
| By: | Zachary Berchenko; Kaizhao Liu |
| Abstract: | For some integer $\ell\geq 2$, consider $m=2\ell-1$ voters, each of which has a preference ranking over $n$ alternatives. The Smith set is the smallest nonempty set of alternatives each of which defeats every alternative outside the set in a pairwise majority comparison. Under the standard benchmark impartial culture where each voter uniformly and independently chooses a random preference ranking over all alternatives, we study the asymptotic probability that the Smith set has cardinality $s$ for fixed $\ell$ and $n\to \infty$. First, we prove that the probability that the Smith set has constant cardinality $s$ goes to zero at a rate of $\Theta_{\ell, s} (n^{-s(\ell-1)/\ell})$. Next, if $\min\{s, n-s\}\to\infty$, we show that this probability decays superpolynomially. Further, when $s$ and $n-s$ are both $\Theta(n)$, we prove that the probability decays exponentially and determine the exact exponential base. Finally, we prove that the probability that the Smith set contains all alternatives approaches one at a rate of $\Theta_\ell(n^{-(\ell-1)/\ell})$. These theorems resolve the conjectures in [Liu et al, Ann Stat 2026] under impartial culture. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.03814 |
| By: | Jo\~ao Thereze (Fuqua School of Business, Duke University); Udayan Vaidya (Fuqua School of Business, Duke University) |
| Abstract: | We take a revealed-preference approach to study the welfare effects of price discrimination. An analyst observes price and quantity data before and after a monopolist segments the market. The analyst knows neither the aggregate demand curve nor the information available to the monopolist. We characterize the set of observable price-quantity pairs that are rationalizable by some market segmentation. We then obtain sharp bounds on the change in consumer surplus arising from some segmentation. Finally, we provide conditions under which the data identifies an unambiguous increase (decrease) in consumer surplus. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10172 |
| By: | Kurt R. Brekke; Odd Rune Straume; Lars Sørgard |
| Abstract: | Book markets are characterised by common distribution through competing bookstores and vertical integration between publishers and bookstore chains, and in many countries publishers are allowed to set fixed book prices (FBP) in the bookstores. Under vertical separation, FBP can reduce retail prices when publishers have sufficiently strong bargaining power, as the elimination of double marginalisation outweighs the loss of intra-brand competition. We show that vertical integration fundamentally changes this trade-off. It eliminates double marginalisation inside the chain, thereby substantially reducing the scope for FBP to lower retail prices. But since FBP eliminates retail price differences on the same title, the allocative distortions are reduced when imposing FBP and consumer welfare and total welfare are no longer aligned. We find that, in the presence of vertical integration, the introduction of FBP is less likely to benefit consumers and more likely to benefit publishers than in an industry with vertical separation. |
| Keywords: | fixed book prices, vertical integration, double common agency |
| JEL: | D43 K21 L42 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13042 |
| By: | Tim Wienand; Brice Magdalou; Richard Nock; Paul Hufe |
| Abstract: | We develop a framework to evaluate income distributions from the perspective of an opportunity-egalitarian social planner. Through an original axiomatic route that bridges normative economics and decision theory under ambiguity, we characterize a class of social welfare functions governed by a single parameter capturing the planner's aversion to inequality of opportunity. We obtain a `mean-divergence' representation that separates economic efficiency from a penalty for inequality of opportunity, as well as a stochastic dominance criterion for robust welfare comparisons. We apply these theoretical results to analyze opportunity-sensitive social welfare in the United States across birth cohorts and regions. Mapping standard estimates of intergenerational mobility into our framework, we show that welfare rankings vary substantially with the assumed degree of inequality-of-opportunity aversion. We transparently gauge the extent of this normative ambiguity by providing bounds on the ranking of birth cohorts and regions, respectively. |
| Keywords: | inequality of opportunity, intergenerational mobility, welfarism, utilitarianism, social welfare measurement |
| JEL: | D31 D63 I31 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13034 |
| By: | Steve Lawford |
| Abstract: | When manuscripts become cheap to produce but expert evaluation stays scarce, submission rights acquire value. A non-transferable author quota turns submission into a revealed-priority decision: authors nominate their top projects using only ordinal information, and, with informative rankings, adding candidates cannot worsen the selected portfolio. The cost is inflexibility in allocating review capacity across authors and realised projects. In a tractable benchmark, I derive the exact equal-load condition under which the quota's robustness to heterogeneous fee sensitivity and cardinal miscalibration outweighs that cost. With bounded project values, abundance can turn an equal-load fee into an access screen, while the quota preserves within-author curation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.04688 |
| By: | David Argente |
| Abstract: | Complementarities can have important welfare consequences, but quantifying these effects would seem to require identifying and valuing the underlying mechanisms separately. This paper shows that this need not be the case. I provide necessary and sufficient conditions under which baseline subsidized activity and the direct and total responses to a subsidy determine aggregate willingness to pay. A sufficient condition for valuing the equilibrium adjustment is that it has the same effect on utility as an additional subsidy common to all agents and relevant actions. The formula is easy to apply to existing estimates and guides the design of new experiments. |
| JEL: | D6 H2 H4 O2 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35843 |
| By: | Johann Caro-Burnett; Sebastian Galiani; Gustavo Torrens |
| Abstract: | Why do rising powers survive periods in which established states can still suppress them? Existing theories of preventive war emphasize commitment problems between declining and rising states, which can make adverse power shifts especially dangerous. We show that commitment problems among established rivals can have the opposite effect. Preventive action against a rising power can alter the incumbent’s relationship with another state. Under opportunistic rivalry, prevention temporarily exposes the incumbent to exploitation by an existing rival. Under defensive rivalry, successful prevention strengthens the incumbent by eliminating a potential counterweight, giving its rival an incentive to protect the rising state. In both cases, third-party responses can deter preventive action that would occur in an otherwise identical dyadic setting. Cooperation among established powers can reverse this result when credible arrangements allow them to manage the strategic consequences of suppression. Historical evidence from the American Revolution, China’s nuclear emergence, and U.S.–Soviet bargaining over West German nuclear capabilities illustrates the mechanisms and their limits. The analysis shows how rivalry among established powers can protect vulnerable rising states and thereby facilitate changes in the international distribution of power. |
| JEL: | P0 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35862 |
| By: | Jun Yeong Lee |
| Abstract: | Evidence that pricing algorithms collude comes from markets in which every seller runs the same algorithm. We ask what happens when they do not. Four language models from four providers, each at its cheapest tier, price in a four-firm logit Bertrand market without communication, in every homogeneous, two-by-two and fully mixed composi- tion (11 cells, 20 runs, 200 periods). Collusion is a property of the model: Claude and Gemini markets reach 72 to 79 percent of the monopoly rent, DeepSeek markets 24 percent, and GPT markets none, though GPT prices drift above the monopoly level rather than toward competition. Mixing does not reduce collusion by itself. Markets containing Gemini, which opens at the highest price and settles highest, are more col- lusive than the homogeneous markets they are built from; markets containing Claude, which opens lower and follows its rivals down, are less so; and only the fully mixed market is significantly less collusive than the average homogeneous one. Stability de- pends on the least stable participant: two GPT firms suffice to keep any market from converging. Inside mixed markets the rent is shared in a transitive order, DeepSeek over Claude over Gemini over GPT, that inverts the anchor ranking. The model that raises the price collects the least of the rent, as the price-leadership model predicts. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11256 |
| By: | Qi-Qing Song; Jia-Lin Liu; Jia-Yu Cui |
| Abstract: | This paper investigates the non-emptiness of the fuzzy core and introduces the notion of the TU-fuzzy core for pure exchange economies with discontinuous utility functions. We propose two stability conditions: local fuzzy-coalition stability and local TU-fuzzy-coalition stability. We also introduce an independent-$\pi$-balanced family of subsets of the agent set to construct two payoff-dependent NTU games. These constructions serve as bridges linking the fuzzy core, the TU-fuzzy core, and NTU games. Under the proposed stability conditions, we establish the non-emptiness of the fuzzy core for economies with quasi-concave utility functions and the non-emptiness of the TU-fuzzy core for economies with concave utility functions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06572 |
| By: | Jacob Goldin; David Weisbach |
| Abstract: | Line drawing is a pervasive feature of legal systems. Across many domains, the applicable legal treatment turns on whether an activity falls above or below some threshold. We characterize the economic forces that determine the optimal placement of such thresholds, both generally and in specific legal settings involving monetary and non-monetary sanctions, prohibitions, and mandates. We apply our results to two important line-drawing questions in private law: the optimal due-care threshold for negligence liability and the optimal threshold for whether a shortfall in contract performance constitutes breach. In both applications, the optimal line takes the form of a population-level marginal cost-benefit rule, with the relevant costs and benefits weighted over the actors whose behavior the line induces to change. |
| JEL: | H0 K1 K12 K13 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35868 |