Factorised Active Inference for Strategic Multi-Agent Interactions

Abstract: Understanding how individual agents make strategic decisions within collectives is important for advancing fields as diverse as economics, neuroscience, and multi-agent systems. Two complementary approaches can be integrated to this end. The Active Inference framework (AIF) describes how agents employ a generative model to adapt their beliefs about and behaviour within their environment. Game theory formalises strategic interactions between agents with potentially competing objectives. To bridge the gap between the two, we propose a factorisation of the generative model whereby each agent maintains explicit, individual-level beliefs about the internal states of other agents, and uses them for strategic planning in a joint context. We apply our model to iterated general-sum games with two and three players, and study the ensemble effects of game transitions, where the agents' preferences (game payoffs) change over time. This non-stationarity, beyond that caused by reciprocal adaptation, reflects a more naturalistic environment in which agents need to adapt to changing social contexts. Finally, we present a dynamical analysis of key AIF quantities: the variational free energy (VFE) and the expected free energy (EFE) from numerical simulation data. The ensemble-level EFE allows us to characterise the basins of attraction of games with multiple Nash Equilibria under different conditions, and we find that it is not necessarily minimised at the aggregate level. By integrating AIF and game theory, we can gain deeper insights into how intelligent collectives emerge, learn, and optimise their actions in dynamic environments, both cooperative and non-cooperative.