Ethnographic and historical data reveal a great diversity of economic organizations, among which market and scarcity are but one set of guidelines for our interaction with humans and non-humans. To expand the space of possible economic models, I propose to complement the individualistic framework of decision theory with a grammar of \textit{social roles}: positions and relationships through which the collective guides the actions, the perceptions, and even the desires of its agents.
In this grammar, I show that a minimal set of rules is needed to sketch out a vast array of economic ``worldviews'', from profit-driven resource exploitation to webs of personal obligations and animistic trade with natural entities. The formalism then allows to compute the utility and strategy space associated with each position in a social structure, giving a precise meaning to the influence of context on economic behavior.
Previous mathematical approaches have often required modellers to make \textit{ad hoc} choices of strategies and payoffs to describe specific socio-cultural settings, with no principled theory to rely upon. This work is meant as a first step toward a common language for interfacing qualitative cultural knowledge with decision theory, and systematically exploring the potential of various settings for conflicts, dilemmas and change.