Decision theorists distinguish between choice under uncertainty and choice under risk. In the latter case, the decision maker has probabilistic information about the possible states of the world. In the former case, there is no such information. There is an extensive literature concerning decision making in both types of situations (see Peterson 2009 for a discussion and pointers to the relevant literature). In the setting of epistemic game theory, the appropriate notion of a “rational choice” depends on the type of game model used to describe the informational context of the game. So, in general, “rationality” should be read as following a given choice rule. The general approach is to start with a definition of an irrational choice (for instance, one that is strictly dominated given one’s beliefs), and then define rationality as not being irrational. Some authors have recently looked at the consequences of lifting this simplifying assumption (cf., the tripartite notion of a categorization in Cubitt &amp; Sugden (2011) and Pacuit &amp; Roy (2011)), but the presentation of this goes beyond the scope of this entry.