  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.
  Another set of issues has to do with the fundamental meaning of prices and
the related question of what the observables 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. We review some of their work and provide a
sketch of how gauge invariance can be incorporated into the formulation of
agent based models.
