States in a game model not only represent the player’s beliefs about what their opponents will do, but also their higher-order beliefs about what their opponents are thinking. This means that outcomes identified as “rational” in a particular informational context will depend, in part, on these higher-order beliefs. Both game theorists and logicians have extensively discussed different notions of knowledge and belief for a group, such as common knowledge and belief. In this section, we briefly recount the standard definition of common knowledge. For more information and pointers to the relevant literature, see Vanderschraaf &amp; Sillari (2009) and Fagin et al., (1995: ch. 6).