A quantitative assessment of the global importance of an agent in a team is
as valuable as gold for strategists, decision-makers, and sports coaches. Yet,
retrieving this information is not trivial since in a cooperative task it is
hard to isolate the performance of an individual from the one of the whole
team. Moreover, it is not always clear the relationship between the role of an
agent and his personal attributes. In this work we conceive an application of
the Shapley analysis for studying the contribution of both agent policies and
attributes, putting them on equal footing. Since the computational complexity
is NP-hard and scales exponentially with the number of participants in a
transferable utility coalitional game, we resort to exploiting a-priori
knowledge about the rules of the game to constrain the relations between the
participants over a graph. We hence propose a method to determine a
Hierarchical Knowledge Graph of agents' policies and features in a Multi-Agent
System. Assuming a simulator of the system is available, the graph structure
allows to exploit dynamic programming to assess the importances in a much
faster way. We test the proposed approach in a proof-of-case environment
deploying both hardcoded policies and policies obtained via Deep Reinforcement
Learning. The proposed paradigm is less computationally demanding than
trivially computing the Shapley values and provides great insight not only into
the importance of an agent in a team but also into the attributes needed to
deploy the policy at its best.

本文提出了一种基于 Shapley 分析实现多智能体系统中个体贡献度评估的方法，并利用层次化知识图谱用于降低计算复杂度，同时通过测试证明了该方法不仅能评估团队中个体的重要性，还能揭示实现最佳策略所需的特征属性。

利用 Myerson 值更高效地计算合作多智能体系统的个人属性和政策贡献，以实现事后解释

Towards a more efficient computation of individual attribute and policy contribution for post-hoc explanation of cooperative multi-agent systems using Myerson values

This paper introduces a novel approach that enables a number of cognitive
radio devices that are observing the availability pattern of a number of
primary users(PUs), to cooperate and use \emph{Bayesian nonparametric}
techniques to estimate the distributions of the PUs' activity pattern, assumed
to be completely unknown. In the proposed model, each cognitive node may have
its own individual view on each PU's distribution, and, hence, seeks to find
partners having a correlated perception. To address this problem, a coalitional
game is formulated between the cognitive devices and an algorithm for
cooperative coalition formation is proposed. It is shown that the proposed
coalition formation algorithm allows the cognitive nodes that are experiencing
a similar behavior from some PUs to self-organize into disjoint, independent
coalitions. Inside each coalition, the cooperative cognitive nodes use a
combination of Bayesian nonparametric models such as the Dirichlet process and
statistical goodness of fit techniques in order to improve the accuracy of the
estimated PUs' activity distributions. Simulation results show that the
proposed algorithm significantly improves the estimates of the PUs'
distributions and yields a performance advantage, in terms of reduction of the
average achieved Kullback-Leibler distance between the real and the estimated
distributions, reaching up to 36.5% relative the non-cooperative estimates. The
results also show that the proposed algorithm enables the cognitive nodes to
adapt their cooperative decisions when the actual PUs' distributions change due
to, for example, PU mobility.

本文提出了一种新的方法，旨在使多个认知无线电设备协作、使用贝叶斯非参数技术来估计原始用户的活动分布，进而通过形成联盟来优化算法性能，并得到了较高的准确性和性能优越性。