Time and symmetry in models of economic markets

These notes discuss several topics in neoclassical economics and alternatives, with an aim of reviewing fundamental issues in modeling economic markets. I start with a brief, non-rigorous summary of the basic Arrow-Debreu model of general equilibrium, as well as its extensions to include time and contingency. I then argue that symmetries due to similarly endowed individuals and similar products are generically broken by the constraints of scarcity, leading to the existence of multiple equilibria. This is followed by an evaluation of the strengths and weaknesses of the model generally. Several of the weaknesses are concerned with the treatments of time and contingency. To address these we discuss a class of agent based models[3]. Another set of issues has to do with the fundamental meaning of prices and the related question of what the observeables of a non-equilibrium, dynamic model of an economic market should be. We argue that these issues are addressed by formulating economics in the language of a gauge theory, as proposed originally by Malaney and Weinstein[8]. We review some of their work and provide a sketch of how gauge invariance can be incorporated into the formulation of agent based models. ∗[email protected] 1 ar X iv :0 90 2. 42 74 v1 [ qfi n. G N ] 2 5 Fe b 20 09