 The example raises the question just why players should act this way, and whether, say, a more cooperative behavior could also be justified. An answer obviously depends on the players’ information and style of reasoning. Here it becomes of interest to probe the structure of the example. Looking more closely, many notions are involved in the above scenario: actions and their results, players knowledge about the structure of the game, their preferences about its results, but also how they believe the game will proceed. There are even counterfactual conditionals in the background, such as A’s explaining his choice afterwards by saying that “if I had played right, E would have played left”. These notions, moreover, are entangled in subtle ways. For instance, A does not choose left because it dominates right in the standard sense of always being better for him, but rather because left dominates right according to his beliefs. How these beliefs are formed, in turn, depends on many other features of the game, including the nature of the players.