There are some strong feelings in the fields of experimental and behavioral economics about the appropriate learning model to use. Which model is right? In my opinion, this is not the right question to ask. All models are wrong. They ought to be. Economic Models are by definition simplified abstractions. They are supposed to be reduced to the simplest core that makes them useful. So then the right question is: "What do you need the learning model for?" The answer for me is varied.
Sometimes, I need the simplest model that can map incentives to dynamic paths, allows flexibility, and can capture behavioral patterns observed in practice. In many cases, this model will come from a class of models known as reinforcement learning. Other times, I would like to parameterize a model in a way that will make it fit a large number of games and settings. Again, reinforcement learning is typically useful.
Other times, I have data that I need to fit from one period to the next. That is, I have data on the entire history of play for a person up to time t, and I want to predict t+1. Reinforcement learning models typically involve few parameters and are intended to capture learning generalities rather than maximize fit. So to maximize fit, I will use some fit-maximizing model. Experience Weighted Attraction comes to mind. As I show in my works with Dale Stahl and independently with Ido Erev, EWA's strength in fit comes from its novel (possibly superior) way of modeling action inertia through its delta parameter (you can think of (1-delta) as the degree of action inertia). Unfortunately, much of the profession is convinced that delta is some hybrid parameter that represents the weight on belief learning veruss reinforcement learning. It is very hard to undo that impression and so the real strength of EWA will likely remain a mystery to most people. But the confusion of the field does not detract from the usefulness of EWA as a powerful model, for the right purpose. It is also a fairly straightforward model to implement.
In many situations, human decision makers do not learn over actions (A, B, C ...). They learn to make sense of the environment and to predict their opponents better. In other words, the rules they make to map information to action change over time. This is where rule learning is very useful. Dale Stahl has invented the concept of rule learning and proposed one of the most general classes of rule learning in the literature-- based on hierarchical thinking.
Over the years I have been introduced to genetic algorithms as well (though to my recollection I only published one paper using them, with Utku Unver and Al Roth, see list of papers). Much like reinforcement learning, they are concerned with mapping incentives to dynamic paths and outcomes rather than with fitting individual behavior (which they can't do as far as I know). Like rule learning they can be modified to account for some pretty complex strategies as long as you can break these strategies into their individual components and code each strategy as a binary array.