Applied Rational Choice Theory

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I am a programmer researching the application of Rational Choice Theory. I have found many links to the philosophical nature of it. And fewer documents formalizing it's mathematical principles. ( https://web.stanford.edu/~jdlevin/Econ%20202/Choice%20Theory.pdf )

While these are good resources for a basic understanding, As an engineer, I am looking for resources on how "Rational Choice" models are built.

While my internet searches describe how to formalize their mathematical properties, I am looking for some concrete examples on how to build such a model.

For example: I am sure that someone is using some common regression techniques to find equilibriums, but I have yet to find a good learning resource with examples of how to extract one from the assumptions. Or how would one extract a utility function from given data?

As I don't have an economics background I might be searching for the wrong keywords on google.