In many resource allocation problems, agents' valuations are best interpreted not as subjective preferences, but as the value they generate from receiving resources. Such valuations capture productivity, effectiveness, or technology, and may differ significantly across agents. In these settings, classical fairness notions such as proportionality or envy-freeness fail to reflect agents' heterogeneous contributions to the collective outcome. Motivated by this perspective, we introduce \emph{Shapley Value Fairness (SVF)} for the allocation of divisible goods without monetary transfers. SVF interprets an agent's entitlement as her expected marginal contribution to optimal social welfare, and uses the Shapley value of the associated welfare maximization game as a normative fairness benchmark. We position SVF relative to existing fairness notions and show that it provides a natural bridge between fairness and efficiency in contribution-based environments. Since exact implementation of the Shapley value is generally infeasible without transfers, SVF naturally leads to the problem of finding allocations that approximate this benchmark as well as possible. We provide a systematic worst-case analysis of the achievable Shapley approximation ratio. For general concave valuations, we establish a tight $Θ(\ln n)$ bound. For capped concave valuations with bounded demands, this bound improves to $Θ(\ln D)$, where $D$ is the maximum aggregate demand for any item. For linear valuations, we further refine the bound to $Θ(\min\{k, \ln γ, \ln n\})$ in terms of the number of agent types $k$ and the value fluctuation ratio $γ$, and show that all bounds are asymptotically tight. Regarding per-instance guarantees, we show that a near-optimal approximation allocation can be computed efficiently (with high probability) via sampling for general concave valuations.

翻译：在许多资源分配问题中，智能体的估值最好不被解释为主观偏好，而是他们从接收资源中所产生的价值。此类估值体现了生产力、效率或技术，并且不同智能体之间可能存在显著差异。在这些情境下，诸如比例性或无嫉妒性等经典公平概念未能反映智能体对集体成果的异质性贡献。受这一视角的启发，我们提出了面向无可转移支付的可持续商品的\emph{夏普利值公平性（SVF）}。SVF将智能体的应得份额解释为其对最优社会福利的期望边际贡献，并以相关社会福利最大化博弈的夏普利值作为规范性公平基准。我们考察了SVF与现有公平概念的关系，并表明它在基于贡献的环境中为公平与效率之间提供了自然桥梁。由于在缺乏转移支付的情况下精确实现夏普利值通常不可行，SVF自然引出了寻找尽可能逼近该基准的分配方案的问题。我们对可实现的夏普利近似比进行了系统的、最坏情况下的分析。对于一般凹性估值，我们建立了紧确的$Θ(\ln n)$界。对于具有有界需求的截断凹性估值，该界改进为$Θ(\ln D)$，其中$D$是任何物品的最大总需求。对于线性估值，我们进一步将界细化为关于智能体类型数量$k$和值波动比率$γ$的$Θ(\min\{k, \ln γ, \ln n\})$，并表明所有界都是渐近紧确的。关于逐实例保证，我们证明对于一般凹性估值，可以通过采样高效地（高概率地）计算出一个接近最优的近似分配方案。