When are complements and substitutes dual?

Philip R. Neary

Home/Archive/arXiv

arXiv · 2610.39844

When are complements and substitutes dual?

Philip R. Neary

View original source ↗Read source document ↗Export metadata ↓

Abstract

For binary-action games on bipartite networks, strategic complements and strategic substitutes are one and the same: each can be transformed into the other by relabelling the actions of every player on exactly one side. In this note, I show that bipartiteness is necessary and sufficient for such a relabelling; as a consequence, bipartite networks are precisely those on which every binary-action game with strategic substitutes must have a pure-strategy Nash equilibrium.

Explore related subjects

econ.GN q-fin.EC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Philip R. Neary. 2026-10-29. When are complements and substitutes dual?. https://arxiv.org/abs/2610.39844

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Costs of Early-career Disciplinary Pivots: Evidence from Ph.D. Admissions

Science often advances when researchers pivot from one discipline to another and import new ideas. However, for established researchers, such pivots are associated with fewer publications and citations. Here, we investigate pivoting at the beginning of a research career--doctoral admissions--when the benefits of importing ideas might outweigh the switching costs. Analyzing 171,347 PhD applications at a large research university from 2013 to 2023, we measured the semantic distance between each applicant's prior degree and target program. Applicants who pivot further had lower undergraduate grades and, controlling for academic and demographic predictors, lower admission chances: the average pivot corresponds to a 5.3% lower admission probability (0.80 percentage points). Among enrollees, the average pivoter takes longer to graduate than non-pivoters, with a 10.7% lower graduation hazard, and similar publication and citation counts on average and at the tails. Our results suggest that pivoting at the outset of research careers, even if it benefits research communities, comes with significant costs to individuals.

econ.GN↗

arXiv2026

How Firms Export: An Assignment Theory of Export Organization

This paper develops a model in which direct exporters, indirect exporters, pure intermediaries, and hybrid exporters emerge endogenously from the assignment of products to export platforms. Firms differ in manufacturing and commercial capabilities. Manufacturing capability determines a product's potential profitability, while commercial capability determines how effectively a platform can sell it abroad. Manufacturing activation and product assignments are jointly determined, subject to fixed manufacturing costs, contracting frictions, and increasing organizational costs. Complementarity between manufacturing and commercial capabilities generates positive assortative matching, while organizational diseconomies shape platform scope. Equilibrium allocations can feature manufacturers exporting through their own platforms or those of other firms, specialized intermediaries exporting products they do not manufacture, and hybrid firms exporting their own products alongside those manufactured by other firms. The model characterizes how contracting costs, foreign-market attractiveness, and organizational diseconomies affect equilibrium assignments.

econ.GN↗

arXiv2026

The missing price feedback: Why studies overstate local grid peaks from synchronized home batteries under real-time pricing

Existing studies consistently find that home batteries optimized against real-time electricity prices create new load peaks in local distribution grids. This is because all assets respond to the same price signal in sync. However, most of these studies are simulations, and they all treat wholesale prices as exogenous, i.e., unaffected by the battery dispatch. This paper argues that assuming prices to be non-responsive biases the result: in reality, charging in low-price hours raises the wholesale price, which dampens the incentive to charge. In equilibrium, charging is spread out across hours. I test this by simulating households with rooftop solar and home batteries under a spot-based retail tariff with a model of equilibrium wholesale prices, calibrated to German data for 2025. With exogenous prices, my results confirm the literature findings: synchronous charging pushes the coincident import peak of the local grid to 83 % above its no-battery level. With endogenous prices, the same fleet leaves the peak 6 % below the no-battery benchmark. This finding is robust across alternative price functions and exogenous price paths, different measures of the coincident peak, 22 scenario variations and three historical years. I conclude that while new local peaks remain possible, particularly in grids that contain local clusters of home batteries, the risk and magnitude are considerably smaller than the existing literature suggests.

econ.GN↗