# Attribution Markets: A Fisher-Market Formulation for Fractional Credit Assignment Between Planned Tasks and Performed Actions

arXiv: https://arxiv.org/abs/2607.20694 · HTML: https://mlsanity.com/paper/2607.20694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 14 of 14)

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- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [A Survey of Temporal Credit Assignment in Deep Reinforcement Learning](https://mlsanity.com/paper/2312.01072/) (2023)
- [Entity Matching using Large Language Models](https://mlsanity.com/paper/2310.11244/) (2023)
- [Multiplicative Pacing Equilibria in Auction Markets](https://mlsanity.com/paper/1706.07151/) (2017)
- [CausalMTA: Eliminating the User Confounding Bias for Causal Multi-touch Attribution](https://mlsanity.com/paper/2201.00689/) (2021)
- [Online Market Equilibrium with Application to Fair Division](https://mlsanity.com/paper/2103.12936/) (2021)
- [Unbalanced Low-rank Optimal Transport Solvers](https://mlsanity.com/paper/2305.19727/) (2023)
- [Statistical Inference for Fisher Market Equilibrium](https://mlsanity.com/paper/2209.15422/) (2022)

## Abstract (arXiv)

Personal and organizational planning systems maintain two records that drift apart: what was planned (a task's effort budget) and what was done (a logged action's duration and description). Existing systems bridge them with an exclusive, all-or-nothing link that strands genuinely related but unlinked effort and reports false stalls on active goals. We formulate the bridge as a quasi-linear Fisher market: planned tasks are budget-constrained buyers, performed actions are divisible goods, and a fused text/structural/temporal signal sets each buyer's valuation. Two market instruments - a seller reserve price and a buyer cash option - yield conservation, a hard budget cap, and a provable junk filter as theorems. We extend the market with a concave completion utility discounting progress as a task nears its plan; standard convergence theory for the market's algorithm does not transfer here, resolved by a satiation-threshold fixed point with existence (Brouwer) and local uniqueness under an explicit diagonal-dominance condition, validated empirically on random and adversarial instances. A de-circularized, multi-seed benchmark - observed affinity corrupted independently of the scored ground truth - surfaces a genuine weak spot: the market's sharp, zero-entropy equilibrium is more sensitive to affinity noise than entropy-regularized optimal transport's permanently smoothed one. We resolve this with a one-parameter entropy-regularized generalization unifying the two, plus a noise-adaptive rule for its regularization strength. We report full reproducibility parameters, discuss limitations candidly, and relate the result to multi-touch attribution, optimal transport, and online Fisher-market algorithms.