Well, there are a lot of options available such as C++, Matlab, Python etc. but it depends upon the scenario and requirements of economic analysis as well to opt for the most suitable language. C++ has been suggested as the preferred language for the economic analysis. Nevertheless, you may want to consider what your requirements are to assess the suitability of a programming language. Please refer to following links for some references.
Actually I simulate all game theoretical interactions in R, so as to do the statistical analysis directly within the simulation codes. But depending on the population size and nature sometimes I face complexity and processing speed issues.
What exactly do you wanna do? if you have standard multiperson interaction setups, z-tree is the most common environment. it's not an actual programming language and honestly not very intuitive to handle, but still that's what's most commonly used. I also use it for my economic experiments, but I am glad that I have an assistant dealing with the programming. Still, I guess it's far less work to deal with z-tree than programming something similarly powerful with C++ or else. I also heard that a new open source equivalent called o-tree is under preparation, but have no experience with it yet.
I just checked this site: http://www.otree.org/
looks good to me, and I hope the programmers have elimited all the famous z-tree bugs...
I'd strongly support Elina's answer. I conduct experiments myself and know other experimental economists. I think C++, Python, Mathematica or else are really not the right tools. Z-tree is THE standard in experimental economics. Programming anything as powerful as z-tree from scratch would take months if not years. Z-tree has its wellknown drawbacks and bugs, but it's still the best (possibly apart from rather new o-tree) software available for conducting economic experiments.