English

Myerson Interaction Index

Optimization and Control 2026-05-28 v1

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.

Cite

@article{arxiv.2605.28529,
  title  = {Myerson Interaction Index},
  author = {Jorge González-Ortega and Elisenda Molina and Juan Tejada},
  journal= {arXiv preprint arXiv:2605.28529},
  year   = {2026}
}