Myerson Interaction Index

Abstract

This paper introduces the Myerson interaction index (MII), an extension of the Shapley interaction index to cooperative games with communication structures restricted by graphs. We establish a formal framework for interaction indices on graphs and provide an axiomatic characterization of the MII based on component efficiency, fairness, and veto partnership consistency. Furthermore, we analyse network-induced interaction to distinguish between effects arising from the graph topology and those stemming from the game's intrinsic synergies. This framework offers a robust tool for analysing coalitional behaviour in structured environments, with potential applications in social network analysis and explainable artificial intelligence.