AI 中文总结
该研究针对在线多智能体契约模型，设计了子模收益下O(1)竞争力的在线策略，还证明了子模与XOS收益在在线契约场景下的竞争力界限存在本质分离。
AI 中文摘要
我们引入并研究多智能体契约模型的在线变体。在该模型中，智能体逐个到达，且以一定概率处于活跃状态。当智能体i到达时，委托人提供线性契约α_i，规定委托人收益中转移给智能体i的比例。智能体可选择付出努力或不付出，付出努力则会产生成本；付出努力的智能体集合通过收益函数f决定委托人的期望收益。所有智能体到达后，智能体形成（纯策略）纳什均衡。我们的主要结果是，针对子模收益，设计了与离线最优相比具有O(1)竞争力的策略；同时以两种方式证明该结果是紧的：其一，若要求智能体当场决策，针对子模收益的任何策略都具有Ω((log n)/(log log n)²)的竞争力；其二，对于更广泛的XOS（即分数次可加）收益类，任何在线策略都具有Ω((log log n)/(log log log n))的竞争力。后一结果揭示了子模收益与XOS收益之间令人惊讶的分离：与离线契约设计、先知不等式等相关场景中，子模收益的常数因子保证可扩展至XOS收益不同，在线契约场景将这两类收益区分开来。
英文摘要
We introduce and study an online variant of the multi-agent contract model. In our model, agents arrive one-by-one and are active with a certain probability. Upon arrival of agent $i$, the principal offers a linear contract $α_i$, specifying the fraction of the principal's reward transferred to agent $i$. Agents can either exert effort or not, incurring a cost if they do. The set of agents that exert effort determines the principal's expected reward through a reward function $f$. After all agents have arrived, the agents form a (pure) Nash equilibrium. As our main result we design an $O(1)$-competitive policy for submodular rewards, compared to the offline optimum. We also show that this result is tight in two ways. First, if we require that agents make decisions on the spot, then for submodular rewards any policy is $Ω((\log n)/(\log \log n)^2)$-competitive. Second, for the broader class of XOS (a.k.a., fractionally subadditive) rewards, any online policy is $Ω((\log \log n)/(\log \log \log n))$-competitive. The latter result reveals a surprising separation between submodular and XOS rewards: unlike related settings such as offline contract design and prophet inequalities, where constant-factor guarantees for submodular rewards extend to XOS rewards, the online contract setting separates the two classes.
