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Wednesday, 4 November 2026: 4 new papers, 4 cross-lists and 8 replacements in Theoretical Economics (econ.TH), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
We study two-stage auctions in which bidders privately know their valuation priors and learning costs, while the seller jointly designs information acquisition, continuation allocation, and payments. Revenue maximization requires screening learning costs while satisfying cross-prior incentives, potentially distorting both experimentation and continuation allocation. We derive a revenue representation involving allocated posterior values, virtual learning costs, and prior-dependent rents, and characterize cross-prior incentives through difference inequalities. We establish existence of optimal mechanisms for finite experiment menus and arbitrary prior distributions. With finite prior support, bounded finite-category linear programs approximate optimal revenue at a linear rate while preserving exact dynamic incentive compatibility and interim individual rationality. Their dual yields joint optimality conditions for experimentation, allocation, and payments. A two-prior example demonstrates that efficient continuation can be revenue-suboptimal and that cost-contingent experimentation can strictly increase revenue.
Bankruptcy rules are rules for dividing an insufficient estate among people with different claims. Existing rules assume that the claims are publicly known. When this is not the case, claimants have a strong incentive to claim more than they are due, as bankruptcy rules give larger allocations to claimants with larger claims. A remedy often used by legal systems is to make over-reporting costly by requiring evidence and imposing penalties. But this remedy also increases the legal expenses of proving true claims, which might result in under-reporting. Encouraging true reporting requires fine-tuning of the legal costs. This paper incorporates the costs of supporting both true and false claims into the bankruptcy model. Claimants incur costs for the true and false parts of their claims, with false claims costing at least as much per unit as true claims. The goal is to set cost rates that induce claimants to report their true entitlements, neither more nor less. Whether this is possible depends on the allocation rule. The proportional and constrained equal awards rules cannot guarantee truthfulness at any positive true-claim cost rate; the same holds for constrained equal losses with at least three claimants. For $N\ge2$ claimants, the rule TAL-1/N from the parameterized Talmud family induces truthfulness exactly when the true-claim cost rate is at most 1/N and the false-claim cost rate is at least 1-1/N. This rule is optimal in the sense that its truthful cost region contains that of every piecewise smooth allocation rule: it gives the legal system the maximum possible flexibility in setting the legal costs. For two claimants, TAL-1/2 (aka Contested Garment rule) uniquely attains this optimal region.
We study binary choice under uncertainty when the comparison between two acts can depend on the joint distribution of their realized outcomes. This motivates correlation probabilistic sophistication (CPS), a subjective reduction principle that extends both probabilistic sophistication and Fishburn's nontransitive subjective expected utility. We show how simultaneous event exchangeability elicits a unique solvable finitely additive subjective probability and reduces binary comparisons of acts to induced joint laws. Under convex range, the induced domain coincides with the full finite joint-law domain, allowing the transfer of correlation-utility representations from risk and, under completeness and Strong Independence, correlation expected utility with a skew-symmetric comparison kernel. Under completeness and transitivity, CPS collapses to ordinary probabilistic sophistication. We further extend the framework to multiple small worlds, allowing correlation sensitivity to vary with the source of uncertainty.
Binary choice under risk can depend on how the alternative outcomes are jointly distributed. We show that in a finite outcome space, continuity, completeness, and betweenness impose a local-to-global restriction on this dependence: indifference between two alternatives with one common marginal distribution, however their outcomes are jointly distributed, implies correlation insensitivity for all lotteries supported on the same outcomes. In the correlation-sensitive case, these three axioms alone characterize correlation weighted utility, which combines statewise comparisons with a bilinear function of the marginal lotteries. In the correlation-insensitive case, an additional projective independence axiom yields Fishburn's (1982) skew-symmetric bilinear representation. Strong independence reduces correlation weighted utility to Lanzani's (2022) correlation expected utility representation. We extend the correlation-sensitive characterization to finitely supported lotteries on general metrizable outcome spaces. The resulting framework distinguishes correlation effects from departures from classical independence, and yields testable restrictions linking choices between identically distributed lotteries to correlated Allais behavior.
We study the optimal design of investment subsidies across heterogeneous monopolistic markets subject to a common expected discounted budget. Each producer faces a regular one-dimensional demand diffusion and chooses irreversible capacity expansion through a singular stochastic control problem. The regulator values weighted consumer surplus, producer profits, and an additional benefit from installed capacity, while accounting for the excess cost of raising public funds. We characterize producers' optimal investment responses through free boundaries and reformulate the regulator's stochastic optimization problem as a deterministic optimization over investment boundaries. An integral representation then recovers the optimal subsidy schedules that implement the resulting capacity policies. Under mild conditions on the diffusions, we establish existence of optimal schedules and uniqueness of the induced investment policies. Finally, we characterize the subsidy schedule and provide numerical illustrations.
AI assistants increasingly participate in work that requires employees to exchange information and coordinate decisions. We study how a firm should design this communication when workers' interests conflict with each other's and the firm's. Two workers privately know local conditions and their preferred responses, while the assistant knows aggregate project conditions. The firm discloses project information before workers report and choose their own actions. Transparency improves adaptation but can undermine truthful preference reporting. When workers agree with the firm on the productive direction, coarsening project information under weak coordination can preserve useful preference reporting at a cost in forecast precision. Under strong coordination, the firm instead prefers full project disclosure and factual reports, because preference information induces costly accommodation of private objectives. Under weak coordination, a firm-optimal policy can leave workers worse off than direct exchange; requiring their acceptance can call for further coarsening. Releasing project context after reports can sustain factual communication that early release would prevent. With separate delivery decisions that cannot be revised jointly, endogenous forwarding weakly improves firm-preferred performance over unchanged forwarding and strictly improves it in some environments. Numerical comparisons show that full initial disclosure captures most gains in the aligned environments considered, while further design has greater value when workers can favor opposing directions. The results distinguish the credibility of employees' reports from their organizational value and show how disclosure timing affects both.
We study automated design of strategyproof (SP) mechanisms for randomized facility location on continuous metric graphs, with the objective of minimizing total distance. We develop methods for computing upper and lower bounds on the optimal approximation ratio achievable by SP mechanisms for a given graph and number of agents. For the lower bound, we propose a cost-preserving reduction to a finite domain that yields lower bounds for unrestricted SP mechanisms through linear programming dual certificates. For the upper bound, we introduce finite representations of mechanisms, called piecewise-linear attributions (PL attributions), that mix piecewise-linear deterministic mechanisms using affine weights on a triangulation of the report space. We show that for mechanisms represented by PL attributions, checking SP and an approximation guarantee reduces to finitely many quadratic nonnegativity tests over compact polytopes. With exact arithmetic and comparisons, each verification certifies the proposed property or returns locations where it fails. In addition, we introduce a strengthening of the incentive notion called strong strategyproofness. We show that for fixed component mechanisms and regions of a PL attribution, the strong strategyproofness requirement can be expressed by a finite number of linear constraints on the attribution coefficients. Using these theoretical results, we propose a heuristic procedure for computing an upper bound on the approximation ratio. We compute certified upper and lower bounds on several metric graphs and numerically evaluate the proposed search procedure. Lastly, we show that deterministic SP onto mechanisms on graphs are strongly strategyproof and admit PL attributions. Thus restricting attention to strongly strategyproof mechanisms admitting PL attributions loses no deterministic SP onto mechanisms.
Colonel Blotto is a fundamental resource-allocation game in which two players divide their budgets across battlefields, and the higher allocation on each battlefield wins its value. The problem of computing an equilibrium efficiently has remained unresolved for its classical continuous version with arbitrary budgets and with values that may vary across battlefields but are the same for both players. We give a fully polynomial-time approximation scheme that computes an $\varepsilon$-Nash equilibrium in time polynomial in the input length and $1/\varepsilon$, and nearly linear in the input length for fixed $\varepsilon$. For sufficiently balanced budgets and battlefield values, we also compute exact equilibria in linear time.