规模化机会约束相关均衡计算：面向独占资源分配博弈

中文摘要 AI 辅助

机会约束相关均衡概念为自利型智能体提供了一种鲁棒的协调技术，这些智能体的成本对中央协调者而言具有不确定性，但其计算中所考虑的联合行动数量随智能体数量呈指数增长。我们针对智能体竞争共享资源且资源同时使用不可取或不安全的博弈，提出了一种精确一对一资源分配限制。该限制允许每个资源恰好分配给一个智能体，从而将所考虑的联合行动数量从n个智能体和r个资源下的O(2^(nr))减少到O(n^r)。所得问题在受限联合行动集上求解，同时保留所有与单边偏离相关的激励约束。我们证明了受限问题的可行集恰好是精确一对一分配集中机会约束纯纳什均衡的凸包，从而给出了非空性的充要条件。我们进一步推导了一个充分条件，在该条件下，无限制博弈的所有机会约束纯纳什均衡均被该限制保留。在垂直起降场离场走廊协调场景中的数值实验表明，相对于无限制公式，中位计算时间减少了99.81%，同时实现了等效的协调性能。

英文摘要

The chance-constrained correlated equilibrium concept provides a robust coordination technique for self-interested agents whose costs are uncertain to a central coordinator, but the number of joint actions considered in its computation grows exponentially with the number of agents. We propose an exact-one resource-assignment restriction for games in which agents compete for shared resources and simultaneous use of a resource is undesirable or unsafe. The restriction allows each resource to be assigned to exactly one agent, reducing the number of joint actions considered from O(2^(nr)) to O(n^r) for n agents and r resources. The resulting problem is solved over the restricted joint action set while retaining all incentive constraints associated with unilateral deviations. We show that the feasible set of the restricted problem is exactly the convex hull of the chance-constrained pure Nash equilibria contained in the exact-one assignment set, yielding a necessary and sufficient condition for nonemptiness. We further derive a sufficient condition under which all chance-constrained pure Nash equilibria of the unrestricted game are retained by the restriction. Numerical experiments in a vertiport departure-corridor coordination scenario demonstrate a 99.81% reduction in median computation time relative to the unrestricted formulation while achieving equivalent coordination performance.

发表机构

• The University of Texas at Austin（德克萨斯大学奥斯汀分校）

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