对抗性拥塞团队博弈中的相关随机性与非相关随机性
Correlated vs. Uncorrelated Randomness in Adversarial Congestion Team Games
AI总结：
本文研究对抗性团队零和网络拥塞博弈中共享与独立随机性导致的均衡成本差距，证明能量与时间成本下的比率上界为 O(min(m_c(G),n))，并给出近似最优策略及其最优性条件。
摘要：
我们考虑团队零和网络拥塞博弈，其中 n 个智能体在图 G 上与 k 个拦截者对抗。智能体的目标是最小化其通过 G 中路径发送流量的集体成本，该成本是边成本的聚合；而拦截者的目标是通过提高其中一些边的成本来最大化这一集体成本。为了规避拦截者，智能体通常会使用随机化策略。我们考虑两种情形：相关情形，即智能体可以访问共享的随机源；以及非相关情形，即每个智能体只能访问其自身的随机源。我们研究非相关智能体必须承担的额外成本，具体做法是比较智能体能够共享随机性与不能共享随机性时，在成本最小的 Nash 均衡中智能体所承担的成本。我们考虑智能体的两种自然成本函数，分别衡量投入的能量和时间。我们证明，对于这两种成本函数，均衡时非相关成本与相关成本之比为 O(min(m_c(G),n))，其中 m_c(G) 是 G 的最小割规模。该界远小于最一般情形；在最一般情形中，已知该比率存在一个紧的指数界 Θ((m_c(G))^{n-1})。我们还引入了一组简单的智能体策略，它们是近似最优的智能体策略。随后，我们针对每种成本函数建立了这些策略何时为最优智能体策略的条件，从而展示了我们所研究的两种成本函数之间的内在差异。
英文摘要：
We consider team zero-sum network congestion games with $n$ agents playing against $k$ interceptors over a graph $G$. The agents aim to minimize their collective cost of sending traffic over paths in $G$, which is an aggregation of edge costs, while the interceptors aim to maximize the collective cost by increasing some of these edge costs. To evade the interceptors, the agents will usually use randomized strategies. We consider two cases, the correlated case when agents have access to a shared source of randomness, and the uncorrelated case, when each agent has access to only its own source of randomness. We study the additional cost that uncorrelated agents have to bear, specifically by comparing the costs incurred by agents in cost-minimal Nash equilibria when agents can and cannot share randomness. We consider two natural cost functions on the agents, which measure the invested energy and time, respectively. We prove that for both of these cost functions, the ratio of uncorrelated cost to correlated cost at equilibrium is $O(\min(m_c(G),n))$, where $m_c(G)$ is the mincut size of $G$. This bound is much smaller than the most general case, where a tight, exponential bound of $Θ((m_c(G))^{n-1})$ on the ratio is known. We also introduce a set of simple agent strategies which are approximately optimal agent strategies. We then establish conditions for when these strategies are optimal agent strategies for each cost function, showing an inherent difference between the two cost functions we study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
