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

Abstract: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.

35 pages, 3 figures. Companion technical report with extended treatment of dynamic/forward-looking markets and reinforcement-learning extensions available separately

Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)

arXiv:2607.20694 [cs.LG]

(or arXiv:2607.20694v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.20694 arXiv-issued DOI via DataCite (pending registration)