Frames, contexts, and history-dependent optimization with applications to circular and sustainable economics

Decisions and ideas arise within "contexts", the set of natural and cultural conditions in which organisms live and human activities take place. Moreover, current decisions are dependent to the past. In this paper, we propose a framework which incorporates general history-dependencies, frames and contexts. It is designed to take into account both that history dependencies affect the contexts and that history dependencies are affected by the contexts. These are crucial issues in many domains, including Economics, Law, Artificial Intelligence and Reinforcement Learning. To be able to consider all kinds of phenomena and issues from different areas, history-dependencies are modeled in a very general way through the introduction of a memory function (not necessarily consumption history formation processes as previously in the economic literature). Our modeling is tractable, interpretable within many diverse contexts and allows several simultaneous frames and history dependencies. We obtain optimization results and develop dynamic programming tools to deal with such models, in particular, we show that there exists a solution and the value function is the unique fixed point of the Bellman operator. Since environmental and sustainable variables are influenced by the memory of our past decisions and can be taken as contexts, as a by-product, we furthermore introduce a very general sustainable framework which fits many existing environmental and sustainable models including circular economy models. It provides a basis for future environmental analysis.