Is the dictator game studied by game theory or by decision theory? Is the dictator game/dilemma studied by game theory or by decision theory? I'm not sure because of the lack of other interactive agents.
I would say that the dictator game is of interest to a decision theorist more so than to a game theorist, although the dictator game can be formally modeled in a game theoretic framework. 

Decision theory studies how behavior, especially those that deviate from the rational ideal assumed by standard economic theory, can be modeled, as well as the implications of these behavioral models. 

Game theory, in contrast, focuses more on the interactive aspect of decisions. The fact that the dictator game can be formalized as a game has more to do with the broad applicability of game theory than the dictator game's intrinsic game theoretic value. 

Based on the purpose of your research, you should be looking up references in the behavioral/experimental literature.