The invasion of economic theory by game theory does not seem to have spared any part of microeconomic theory. In this chapter, I intend to give an account of the beneficial contributions of this invasion for a better understanding of parallel behaviour and its more or less collusive nature. Inevitably, attention will be focused on price leadership which is frequently observed in oligopolistic markets.

When leadership is mentioned the Stackelberg model comes to mind. Two firms have quantity strategies and the leader increases his market share (and his profit) by anticipating the follower's behaviour (who takes the leader's output as given). Unfortunately, this model does not adequately explain parallel behaviour such that the announcement by a firm of a new price is very quickly adopted by its competitors. On the one hand, the sequential character of these announcements is neither modelled nor explained. On the other hand, the identity of the leader remains undetermined: the two Stackelberg firms both want to be the leader.

Can one define a non-cooperative equilibrium which incorporates sequential decisions and in which the identity of the leader is endogenous? In the following, I shall describe the progress made, step by step, in order to answer this question. Quite naturally, the first analytical efforts used static games (with or without uncertainty). More recently, the problem has been re-examined in a repeated game framework.

This dynamic approach illustrates the role played by pre-play conventions on the policy to be followed during the game.