Identification of Causal Effects in Multi-Agent Causal Models

In this paper we introduce multi-agent causal models (MACMs) which are an extension of causal Bayesian networks to a multi-agent setting. Instead of 1 single agent modeling the entire domain, there are several agents each modeling non-disjoint subsets of the domain. Every agent has a causal model, determined by an acyclic causal diagram and a joint probability distribution over its observed variables. We study the identification of causal effects, which is the calculation of the effect of manipulating a variable on other variables from purely observational data. More specifically, we extend an existing single agent identification algorithm to multi-agent causal models. Given some assumptions, we provide a technique to calculate the effect of manipulating a variable in agent A on some variables in another agent B, while only communicating informati on concerning variables that are shared by agents A and B and variables that are being studied in that specific query.