I recently ran into some interesting inter-disciplinary research by Michael McBride (UC Irvine); research at the nexus of game theory, culture and religion. Some examples:
A piece on the relationship between wealth and religiosity: “Religious Market Competition in a Richer World.”
And, a recent article from Rationality & Society on norms, structure, and participation in the LDS Church.
I only briefly read/skimmed the above pieces for their central thesis and approach; all of them quite nicely straddle economics and sociology. Here’s McBride’s website with additional papers on networks, culture, public goods etc.
I've met Michael McBride at a number of conferences and he is engaging in some great economics of religion work. Highly recommended!