Multi-agent influence diagrams for representing and solving games

This paper provides a sound and complete graphical criterion for determining strategic relevance, and shows how strategic relevance can be used to detect structure in games, allowing a large game to be broken up into a set of interacting smaller games, which can be solved in sequence.

Abstract

The traditional representations of games using the extensive form or the strategic form obscure much of the structure of real-world games. In this paper, we propose a graphical representation for noncooperative games—multi-agent influence diagrams (MAIDs). The basic elements in the MAID representation are variables, allowing an explicit representation of dependence, or relevance, relationships among variables. We define a decision variable D′ as strategically relevant to D if, to optimize the decision rule at D, the decision maker needs to consider the decision rule at D′. We provide a sound and complete graphical criterion for determining strategic relevance. We then show how strategic relevance can be used to decompose large games into a set of interacting smaller games, which can be solved in sequence. We show that this decomposition can lead to substantial savings in the computational cost of finding Nash equilibria in these games.