Multi-agent influence diagrams (MAIDs) are a popular form of graphical model
that, for certain classes of games, have been shown to offer key complexity and
explainability advantages over traditional extensive form game (EFG)
representations. In this paper, we extend previous work on MAIDs by introducing
the concept of a MAID subgame, as well as subgame perfect and trembling hand
perfect equilibrium refinements. We then prove several equivalence results
between MAIDs and EFGs. Finally, we describe an open source implementation for
reasoning about MAIDs and computing their equilibria.

本文介绍了多智能体影响图的基础概念，引入了子博弈的概念和博弈均衡。同时，证明了多智能体影响图和全局博弈图之间的等价性，并描述了一种开源的实现方法。

多智能体影响图的均衡优化：理论与实践

Equilibrium Refinements for Multi-Agent Influence Diagrams: Theory and  Practice

Nash equilibrium is a popular solution concept for solving
imperfect-information games in practice. However, it has a major drawback: it
does not preclude suboptimal play in branches of the game tree that are not
reached in equilibrium. Equilibrium refinements can mend this issue, but have
experienced little practical adoption. This is largely due to a lack of
scalable algorithms.
Sparse iterative methods, in particular first-order methods, are known to be
among the most effective algorithms for computing Nash equilibria in
large-scale two-player zero-sum extensive-form games. In this paper, we
provide, to our knowledge, the first extension of these methods to equilibrium
refinements. We develop a smoothing approach for behavioral perturbations of
the convex polytope that encompasses the strategy spaces of players in an
extensive-form game. This enables one to compute an approximate variant of
extensive-form perfect equilibria. Experiments show that our smoothing approach
leads to solutions with dramatically stronger strategies at information sets
that are reached with low probability in approximate Nash equilibria, while
retaining the overall convergence rate associated with fast algorithms for Nash
equilibrium. This has benefits both in approximate equilibrium finding (such
approximation is necessary in practice in large games) where some probabilities
are low while possibly heading toward zero in the limit, and exact equilibrium
computation where the low probabilities are actually zero.

通过发展更高效和可扩展的算法，使用稀疏迭代方法的行为扰动来解决不完全信息博弈中的纳什均衡问题，从而实现最优均衡，但不排除博弈树中未到达的子树中存在次优策略。 通过使用平滑方法，能够计算出一个近似的 extensive-form 完美均衡，以解决经典的纳什均衡算法中存在的精度问题。