Efficient representation of state spaces for some dynamic models

Many important economic problems require computation over state spaces that are not hypercubes. Examples include industry models of multi-product differentiated product firms, Bayesian learning problems with noisy signals and real business cycle models with heterogeneous agents. These problems have not been analyzed partly because of the difficulty in efficiently representing their state spaces on a computer. I develop a representation algorithm for the state spaces of the above problems, which potentially allows them to be solved with computational methods such as dynamic programming. I find that using this representation reduces the computation time and space by several orders of magnitude relative to a naïve representation.