The main aim of this volume is to do justice to a literature which has developed itself at the intersection of several disciplines but, unlike others using similar formal instruments (as, for example, growth theory), has not yet been given a systematic reconstruction. To avoid misunderstandings, I want to point out that the material contained in this volume covers the literature using continuous time models in industrial economics, i.e., either optimal control problems or differential games. Covering also dynamic models in discrete time would require at least the same space, or transforming the book into a large survey. Either way, the volume would become hardly useful.

After the adoption of the game theory approach, the analysis of oligopolistic competition has taken a completely new angle as compared to the previous view of industrial economics prevailing until the early 1970s. The revolution generating what we now call the theory of industrial organization (IO) has shed light on topics which had remained at the margin of the discipline for decades, creating from scratch a number of research strands. Some of the topics addressed in these fields of IO – if not all – have an explicit and intuitive dynamic nature. Capacity accumulation, research & development (R&D) and advertising are obvious examples. Yet, the game theory toolkit has included static (often multistage) and repeated games, and Markovian games in discrete time. In static multistage games, time is blackboxed, while repeated games take a time invariant constituent stage game and typically insert time and time discounting to look at critical thresholds of the latter (as in folk theorems investigating the stability of implicit collusion in prices or outputs).

Proper dynamic games in either discrete or continuous time have been seldom used. This is apparent from dominant textbook in IO at different levels (Tirole, 1988; Martin, 1993, 2002; Shy, 1995; Belleflamme and Peitz, 2010), where dynamics in continuous time is usually confined to the exposition of models dealing with R&D races. Even in Fudenberg and Tirole (1986), a relevant portion of the text treats repeated games while most of the remainder looks at R&D competition. A relevant exception is Fudenberg and Tirole (1991), in which differential game theory is presented and complemented with an illustration of oligopoly games with capacity accumulation games.