In the previous chapter, we have analyzed models in which several decision makers interact strategically. They solve interconnected dynamic optimization problems and the strategic nature of the interaction arises because of the assumption that each decision maker (player) is aware of and takes into account the influence of his or her own strategy choice on the decision problems of the other agents. The present chapter deals with interconnected dynamic optimization problems as well, but now we assume that there is no strategic interaction. Every agent's optimization problem depends on an aggregate system variable, which itself is influenced by the actions of all agents together. Nevertheless, every agent takes the dynamic evolution of the aggregate system variable as given: we say that the agents act competitively. These assumptions are usually justified by the fact that there exists a very large number of decision makers (often infinitely many of them), all of which are ‘small’ relative to the size of the entire economy. In such a situation, every individual decision maker can safely neglect his or her own influence on the aggregate system and on the other decision makers' optimization problems.

In the first two sections of this chapter, we present two different definitions of dynamic competitive equilibrium. In section 8.1, the decision makers take the trajectory of the aggregate system variable as given, whereas in section 8.2 they take the law of motion of this variable as given. In sections 8.3 and 8.4, we assume that in addition to the many competitively behaving agents there exists an additional ‘big’ player (typically a policy maker) who is aware of his or her influence on the evolution of the aggregate system and who can also affect the decision problems of the competitive agents. This player is assumed to act like a Stackelberg leader, that is, he or she chooses a strategy before the competitive agents do so.