 In our description of the refinements to the continuous model of PCF in order to guarantee the definability of finite elements at each type, we have progressively come closer to an interactive explanation of computation. For example, the action of a sequential algorithm \(M \to M'\) (Curien 1986: sec. 3.4) exploits an external calling agent which triggers a cycle of requests and responses on input cells leading (possibly) to the emission of an output value. That interaction should be a central notion in the analysis of computation, especially in relation to full abstraction, is perhaps a natural outcome of the observational stance taken in the definition of operational equivalence. Our short account of game semantics starts precisely from an analysis of a general notion of interaction as a motivation to a first formalization of games which is however rich enough to provide a universe for the interpretation of a restricted set of types and terms. Later we shall add to this definition of game and strategies the features needed to express the constraints that allow strategies to characterize precisely higher-order, sequential computations, which is the aim set for denotational semantics by the full abstraction problem. The present account of the conceptual background of game semantics owes much to the work of Abramsky and Curien (Abramsky 1994, 1996, 1997; Curien 2003a).