# Shadow Futures: Contribution Uncertainty and the Self-Reinforcing Market

Author: [Martin Erlic](https://shadow-futures.vercel.app/author/martin-erlic)

- First posted: December 2025
- Revised: July 2026
- DOI: [10.2139/ssrn.6003994](https://doi.org/10.2139/ssrn.6003994)
- SSRN: [Abstract 6003994](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6003994)
- PDF: [Download the full paper](https://shadow-futures.vercel.app/paper.pdf)

## Abstract

Can a market observe productive inputs perfectly and still be unable to learn what those inputs contributed to its rewards? This paper studies adaptive allocation systems in which verified work, effort, measurable quality, cost, foregone income, and capital at risk directly affect reward probabilities, while past reward changes future exposure. I define the market's comparison budget as the cumulative probability mass remaining outside the currently dominant alternative. For a broad class of locally equivalent allocation rules with a common predictable design, finite total comparison makes the complete single-history laws generated by distinct contribution parameters mutually absolutely continuous. No estimator based on one realized market can consistently recover every nonconstant contribution functional, and no test can separate two contribution parameters with vanishing total error. A finite-horizon bound shows that attribution precision is limited by the comparison budget rather than transaction count. Strong reinforcement is a sharp corollary because it exhausts the budget and produces eventual allocation monopoly. With latent position, contribution and position can be exactly observationally equivalent. The unrealized paths needed to separate these explanations are shadow futures. The result does not deny that work or risk matters. It shows that a real causal effect can remain unrecoverable from the path that rewarded it, with implications for platforms, competition policy, entrepreneurship, and merit-sensitive taxation.

## Keywords

increasing returns; path dependence; identification; cumulative advantage; monopoly; antitrust; taxation; redistribution

## JEL codes

C13; C18; D31; D43; D83; D85; H21; L41

## Central result

The comparison budget is cumulative probability mass remaining outside the currently dominant alternative. Under the paper's common-design, local-equivalence, Hellinger-control, and finite-comparison conditions, distinct contribution parameters generate mutually absolutely continuous complete-history laws.

The implication is an identification limit. No estimator based on one realized market can consistently recover every nonconstant contribution functional, and no test can separate two contribution parameters with vanishing total error.

Strong reinforcement is one sharp corollary because it can exhaust the comparison budget and produce eventual allocation monopoly. With latent position, contribution and position can be exactly observationally equivalent.

## Citation

Erlic, Martin. "Shadow Futures: Contribution Uncertainty and the Self-Reinforcing Market." First posted December 2025; revised July 2026. SSRN abstract 6003994. https://doi.org/10.2139/ssrn.6003994.