Abstract:

I define reflexive economics as an approach where we mathematically model self-referential structures. Current mathematical economics does not handle this peculiarity which arises if the modeller is in the modelled system. In reflexive economics the Russell paradox and similar structures are not bugs but features of social systems. I present the first result in a coinductive treatment of infinite games. We rationalize escalation in case of an assumption of infinite ressouces. I discuss how this might affect infinite horizon models in dynamic macroeconomics towards reflexive belief formation and financial bubbles representing Keynes beauty contest. I then discuss the many fields if not the very definition of social science that are defined by various reflexive structures towards a theory of money and economic value. I argue for a much increased abstraction level of social mathematics starting from coalgebras and Scott domains and in need of category theory instead of set theory for the mathematical and biological foundation of economics.