Causes and Strategies in Multiagent Systems

TL;DR

This work builds a formal bridge between structural causal models and multi-agent reasoning by translating a strongly recursive causal model into a causal concurrent game structure (causal CGS). The construction orders agent variables via an agent-rank function and defines states, actions, and transitions so that leaf-states correspond to interventions on the causal model, enabling Halpern–Pearl actual-causality reasoning about collective strategies. A causal strategy profile is introduced to capture the normal behavior implied by the causal model, and rigorous results link HP causality (including but-for and general cases) to the existence of strategies in the CGS that prevent outcomes, thus relating causal attribution to strategic abilities of coalitions. The framework highlights potential for analyzing responsibility in multi-agent settings and suggests several extensions to probabilistic, cyclic, and epistemic variants to broaden applicability and address context uncertainty.

Abstract

Causality plays an important role in daily processes, human reasoning, and artificial intelligence. There has however not been much research on causality in multi-agent strategic settings. In this work, we introduce a systematic way to build a multi-agent system model, represented as a concurrent game structure, for a given structural causal model. In the obtained so-called causal concurrent game structure, transitions correspond to interventions on agent variables of the given causal model. The Halpern and Pearl framework of causality is used to determine the effects of a certain value for an agent variable on other variables. The causal concurrent game structure allows us to analyse and reason about causal effects of agents' strategic decisions. We formally investigate the relation between causal concurrent game structures and the original structural causal models.

Figures (3)

• Figure 1: The causal network for the causal model for the semi-autonomous vehicle example described in Example \ref{['ex:causal model']}.
• Figure 2: The causal CGS of the semi-automated vehicle example. We only show the initial values of the variables of agent rank $0$ in the starting state. In the middle states we only show the variables with agent rank corresponding to that state. We also do not show the transitions to the same state in the leaf-states.
• Figure 3: The causal CGS of the semi-automated vehicle example. The dotted lines indicate actions that are not following the causal strategy profile.

Theorems & Definitions (20)

• definition 1: Causal Model, Causal Setting halpern2016actual
• definition 2: modified HP Definition halpern2016actual
• definition 3: Concurrent Game Structures alur2002alternating
• definition 4: Strategy in Concurrent Game Structures alur2002alternating
• definition 5
• definition 6: States of a causal CGS
• definition 7: Actions in a causal CGS
• definition 8: Transitions in a causal CGS
• definition 9: Evaluation of states in a causal CGS
• definition 10: Causal CGS