AI 中文总结
研究分散环境中补偿设计问题，提出简单无视成本且匿名的边际贡献支付规则，证明其在大市场情形下能保证纯纳什均衡存在且PoA至多为\(2 + o_{\lambda}(1)\)，还扩展到粗相关均衡等多种情况并给出相应结果。
AI 中文摘要
我们引入补偿设计，即在分散环境中设计激励高质量贡献的支付规则的问题。在此，具有单调次模价值函数且预算受限的委托人旨在设计支付规则，而代理人根据其私人成本决定是否参与。我们表明，一种简单的无视成本且匿名的边际贡献支付规则可确保在大市场情形（\(\lambda \to 0\)，即每个个体成本至多为预算的\(\lambda\)分之一）下纯纳什均衡始终存在且无政府价格（PoA）至多为\(2 + o_{\lambda}(1)\)。我们进一步表明，在确定性无视成本规则中，因子\(2\)是不可避免的。令人惊讶的是，我们发现一个反例表明基于夏普利值的支付规则可能不存在纯纳什均衡。接着我们将范围扩展到粗相关均衡。这是由我们的难解性结果进一步推动的：尽管纯纳什均衡始终存在，但计算它是PLS完全问题。我们证明粗相关均衡的PoA界限也至多为\(2 + o_{\lambda}(1)\)，并且即使在夏普利值诱导的支付规则下该保证也成立。此外，我们超越了单调次模价值函数和二元行动。首先，对于（单调）XOS估值，我们表明没有神谕高效的支付规则能达到\(O(n^{1/2 - \epsilon})\)的PoA界限。其次，对于次模但非单调估值，我们表明一大类自然支付规则无法保证有界的PoA。最后，我们将补偿设计扩展到每个代理人有组合行动集的情形。我们为次可加值提供了具有对数PoA保证的随机支付规则，以及即使在单代理人加值情形下也适用的匹配下界。
英文摘要
We introduce compensation design, the problem of designing payment rules that incentivize high-quality contributions in decentralized environments. Here, a budget-constrained principal with a monotone submodular value function aims to design a payment rule, while agents decide whether to opt in or out depending on their private cost. We show that a simple cost-oblivious and anonymous marginal-contribution payment rule guarantees that pure Nash equilibria always exist and attain a price of anarchy (PoA) of at most $2+o_λ(1)$ in the large-market regime ($λ\to 0$) where each individual cost is at most a $λ$ fraction of the budget. We further show that the factor $2$ is unavoidable among deterministic cost-oblivious rules. Surprisingly, we identify a counterexample showing that a payment rule based on the Shapley value may admit no pure Nash equilibria. We then extend our scope to coarse correlated equilibria. This is further motivated by our intractability result: although a pure Nash equilibrium always exists, computing one is PLS-complete. We establish that coarse correlated equilibria also attain a PoA bound of at most $2+o_λ(1)$, and this guarantee in fact extends even under the payment rule induced by the Shapley value. Moreover, we move beyond monotone submodular value functions and binary actions. First, for (monotone) XOS valuations, we show that no oracle-efficient payment rule can attain a PoA bound of $O(n^{1/2 - ε})$. Second, for submodular but non-monotone valuations, we show that a broad class of natural payment rules fails to guarantee a bounded PoA. Finally, we extend compensation design to the setting where each agent has a combinatorial action set. We provide randomized payment rules with logarithmic PoA guarantees for subadditive values, and matching lower bounds that apply even in the single-agent additive-value setting.
