The models introduced below describe the players’ hard and soft information in interactive situations. They differ in their representation of a state of the world, but they can all be broadly described as “possible worlds models” familiar in much of the philosophical logic literature. The starting point is a non-empty (finite or infinite) set \(S\) of states of nature describing the exogenous parameters (i.e., facts about the physical world) that do not depend on the agents’ uncertainties. Unless otherwise specified, \(S\) is the set of possible outcomes of the games, the set of all strategy  profiles.[6]  Each player is assumed to entertain a number of possibilities, called possible worlds or simply (epistemic) states. These “possibilities” are intended to represent a possible way a game situation may evolve. So each possibility will be associated with a unique state of nature (i.e., there is a function from possible worlds to states of nature, but this function need not be 1–1 or even onto). It is crucial for the analysis of rationality in games that there may be different possible worlds associated with the same state of nature. Such possible worlds are important because they open the door to representing different state of information. Such state-based modeling naturally yields a propositional view of the agents’ informational attitudes. Agents will have beliefs/knowledge about propositions, which are also called events in the game-theory literature, and are represented as sets of possible worlds. These basic modeling choices are not uncontroversial, but such issues are not our concern in this entry.