Part III Competitive equilibria and applications Chapter 7 Recursive (Partial) Equilibrium . An equilibrium concept This chapter formulates competitive and oligopolistic equilibria in some dynamic settings. Up to now, we have studied single-agent problems where components of the state vector not under the control of the agent were taken as given. | Part III Competitive equilibria and applications Chapter 7 Recursive Partial Equilibrium . An equilibrium concept This chapter formulates competitive and oligopolistic equilibria in some dynamic settings. Up to now we have studied single-agent problems where components of the state vector not under the control of the agent were taken as given. In this chapter we describe multiple-agent settings in which some of the components of the state vector that one agent takes as exogenous are determined by the decisions of other agents. We study partial equilibrium models of a kind applied in We describe two closely related equilibrium concepts for such models a rational expectations or recursive competitive equilibrium and a Markov perfect equilibrium. The first equilibrium concept jointly restricts a Bellman equation and a transition law that is taken as given in that Bellman equation. The second equilibrium concept leads to pairs in the duopoly case or sets in the oligopoly case of Bellman equations and transition equations that are to be solved jointly by simultaneous backward induction. Though the equilibrium concepts introduced in this chapter obviously transcend linear-quadratic setups we choose to present them in the context of linear quadratic examples in which the Bellman equations remain tractable. 1 For example see Rosen and Topel 1988 and Rosen Murphy and Scheinkman 1994 186 Example adjustment costs 187 . Example adjustment costs This section describes a model of a competitive market with producers who face adjustment The model consists of n identical firms whose profit function makes them want to forecast the aggregate output decisions of other firms just like them in order to determine their own output. We assume that n is a large number so that the output of any single firm has a negligible effect on aggregate output and hence firms are justified in treating their forecast of aggregate output as unaffected by their own output .
