Many neuroeconomics studies use fMRI machines. In my group, we currently concentrate on the electroencephalograph (EEG). The main reason is that we are interested in the analysis of decision processes in the brain, and the EEG has an excellent time resolution, while the fMRI is better for questions requiring a fine spatial resolution, e.g. brain localization.
An example of what the EEG can do for economic research, and in particular decision theory, is in a paper from my lab (Achtziger, Alós-Ferrer, Hügelschäfer, and Steinhauser, 2014), published in the journal Social Cognitive and Affective Neuroscience (with the lovely acronym SCAN). In case you are wondering, authors are in alphabetical order as per econ conventions; unlike neuroscientists, economists do not quibble about who has contributed more to a given paper.
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