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I have some scenarios I would like to model using rational choice theory (i.e. utility maximizing agents). For example, a two population type (I suspect this means two representative agents), two good, multi period model with trading. In particular, none of the scenarios I have in mind should require strategic behavior, so I think I should be able to avoid game theory.

I have a reasonable idea of how to describe such a model, but less of a sense about how to solve it and under what conditions it would have an analytic solution.

What book/website would help me learn the techniques, tricks and tropes used in applied rational choice modeling? I have a solid basic math background (multi-variable calculus, ODE/PDEs, mathematical statistics).

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