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

TL;DR

This paper advances the theory of multi-agent influence diagrams by introducing subgame concepts and equilibrium refinements, providing new insights and tools for analyzing complex multi-agent decision problems.

Contribution

It introduces the concept of MAID subgames and equilibrium refinements, establishing equivalences with extensive form games and providing an open-source reasoning implementation.

Findings

Defined MAID subgames and equilibrium refinements

Proved equivalence results between MAIDs and EFGs

Provided an open-source tool for MAID analysis

Abstract

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.