Brian Epstein & Ryall - Broadening Formal Models of Individual and Collective Intentionality

Game theory models situations in which a set of forward-looking agents make interactive decisions. The building blocks of game theory are general and parsimonious. They enable game theory to model a broad range of phenomena with elegant mathematical structures. That said, the field does face some notable challenges.
One set of challenges involves modelling the epistemic limitations of real-world decision makers. For example, a particular cognitive bias observed by psychologists will be modelled by making particular modifications to a standard model. At present there is no general model of bounded cognition that explains all or even a wide range of known biases. Another example is modelling meso-scale social phenomena, such as groups, firms, and institutions. Institutions and organizations are widely studied in game theory, but typically as aggregates of agents coordinating with one another. Yet coordination only accounts for some of the many cohesive features of institutions and organizations.
One feature that is present in the lion’s share of game theory work is its implicit belief-desire approach to modelling mental states. In philosophy, many scholars argue that more elaborate models of cognition and action are essential for explaining the practical reasoning and behaviors of individuals. Intention is the most widely discussed mental state argued to contribute to practical activity of agents. Yet, it is only one of many, including plans, reliance and so on. Some of this work has been incorporated in computational models of interacting agents, but little has been adopted into game theory proper.
In social ontology, even reductive accounts of group agency are typically built from individuals with a wide range of cognitive states, not just beliefs and desires. And both reductive and non-reductive accounts theorize about features of groups that appear to be distinct from features that aggregates of coordinating agents would possess—features such as group-level attitudes.
The project of which this paper is a part aims to approach game theory with a more elaborate ontology of mental states, informed by work in action theory and social ontology. Rather than reducing multi-scale social phenomena to groups of coordinating agents or representing the epistemic limitations via ad-hoc modifications to a belief-desire model, we accept a richer set of building blocks at the outset. With these, we treat the cognitive lives of limited individuals and groups in greater detail, and hope to provide more systematic explanations of the sort of game theoretic challenges described above. We also clarify and correct claims in action theory about relations among cognitive states of individuals, as well as between individuals and social groups.
In this paper, we sketch the foundations of a mathematical framework in which intentions perform two broad functions. First, as is widely discussed, intentions improve the efficiency of agents with epistemic limitations. Second, individual intentions perform a social function: pairs or groups of agents who possess individual intentions may induce behaviors that are unavailable to belief-desire agents. We also begin to extend this to a formal theory of groups, including group formation and persistence, as well as aspects of group cognition. Our framework lends itself to addressing issues that the formal literature on agency (such as the BDI literature in logic and computer science) has not been able to treat, such as plan revision in a social context and in response to the plans of others.