Economics: when assumptions determine what a model can tell us

The connecting question: what does the result establish?

This week’s selected coverage links two problems: whether a strategic model admits the proposed solution, and whether an empirical method supports the intended causal conclusion. The connections are methodological, not evidence of consensus. Auction counterexamples and network existence theorems concern different solution concepts; distributional tests and threshold-based estimates answer different empirical questions. Reading them together makes the scope of each result central, rather than treating existence, significance or a near-zero estimate as an endpoint.

Existence depends on the model and solution concept

The multiunit-auction paper constructs independent, full-support type distributions that defeat monotone pure-strategy equilibrium when at least one bidder is strictly risk averse. For uniform pricing, the result covers every supply of at least three units and both standard pricing rules, subject to admissibility; for discriminatory pricing, it constructs a finite supply with nonexistence. This is a counterexample-based limit on a familiar class of bidding strategies—not a claim that every risk-averse auction lacks equilibrium, or that all equilibrium concepts fail (multiunit auctions).

The dynamic-games paper identifies a different boundary. For continuous dynamic games with perfect information, weak atomic continuity of Nature’s transition probabilities, together with the paper’s other regularity assumptions, guarantees measurable pure-strategy subgame-perfect equilibrium for finite and infinite horizons. If that condition fails, the authors can construct a game without subgame-perfect equilibrium even in behavioral strategies. The necessity is for a guarantee across the remaining game primitives, not a statement that every game violating the condition fails (dynamic games).

By contrast, the network paper proves existence of coalitionwise stable networks under continuity and componentwise quasiconcavity, allowing continuous interaction weights, coalition capacities and individual budgets. Feasibility couples interactions: perturbing one can make another infeasible. Its constrained stability refinements address that complication (weighted networks). These positive results do not rebut auction nonexistence. They concern different feasible choices, deviations and solution concepts; the shared lesson is to inspect those definitions before comparing conclusions.

Risk preferences: a related topic, not a shared mechanism

The correlation-preference paper asks whether binary choices depend on the joint distribution of alternatives’ outcomes, rather than only their separate distributions. On a finite outcome space, continuity, completeness and betweenness impose a local-to-global restriction: indifference across every coupling at one full-support lottery rules out correlation sensitivity for all lotteries supported on those same outcomes. In the correlation-sensitive case, the axioms characterize correlation weighted utility. The separate extension to general metrizable outcome spaces concerns the correlation-sensitive characterization for finitely supported lotteries, not an unrestricted extension of that local-to-global claim (correlation preferences).

This connects to auctions through the modeling of risky choice, but correlation sensitivity and risk aversion are not interchangeable assumptions. The paper supplies axiomatic restrictions and testable implications, not evidence that auction bidders exhibit the characterized preferences. An unresolved empirical question is how actual choices fit those restrictions; the selected evidence does not settle it.

Detecting effects versus estimating a local effect

The conditional-independence paper tests whether outcomes improve prediction of treatment assignment beyond covariates alone. It proposes inverse-propensity-weighted, double-residualization and augmented-weighting approaches. With known propensity scores, its conditional randomization procedure controls size in finite samples. Reported simulations show power gains over a joint Wald benchmark in several nonlinear settings, including effects with opposite signs. But the supplied small-sample comparisons with weak treatment effects are complementary, not a uniform power ranking: DR, AIPW and DR-star dominate when the treatment effect averages to zero, while KCI, GCM and joint Wald tests dominate when the mean treatment effect is nonzero (conditional-independence tests).

The causal interpretation requires unconfoundedness; predictive information alone does not remove unmeasured confounding. The target is a joint distributional effect, not its sign or magnitude. The RD guide instead explains identification using comparisons near a treatment threshold, conditional on comparability and other design assumptions. Manipulated scores or another intervention changing at the same cutoff can undermine interpretation (RD guide). Testing distributional differences and establishing credible threshold-based identification therefore solve different problems.

The guide’s medical illustration also separates uncertainty from generalization. It reports a complier effect of contrast-enhanced CTPA on long-term kidney function of −0.4 mL/min/1.73 m², with a 95% confidence interval from −4.9 to 4.0. The interval permits both decreases and increases in eGFR; the supplied evidence does not establish their clinical importance. The estimate concerns patients near the cutoff whose treatment changes with the rule, not all patients (RD interpretation).

Evidence limits

All six sources include selected paper-text excerpts and abstracts, not complete-paper review. Extraction visibly disrupts some equations and tables, so those fragments do not support independent reconstruction of proofs or numerical comparisons. Abstract-only claims are kept at abstract-level detail; missing excerpted material is not evidence of absence from a paper. The arXiv versions include preprints whose publication status is not otherwise established here; the RD manuscript explicitly states online publication in JAMA. These limits leave proof details, empirical applicability and broader generalization open rather than resolved by this selection.