Living Reference Work Entry

Handbook of Dynamic Game Theory

pp 1-44

Date: Latest Version

Infinite Horizon Concave Games with Coupled Constraints

  • Dean CarlsonAffiliated withMathematical Reviews, American Mathematical Society Email author 
  • , Alain HaurieAffiliated withORDECSYS and University of GenevaGERAD, HEC Montreal
  • , Georges ZaccourAffiliated withGERAD, HEC MontrealDépartement de sciences de la décision, GERAD, HEC Montreal


In this chapter, we expose a full theory for infinite-horizon concave differential games with coupled state-constraints. Concave games provide an attractive setting for many applications of differential games in economics, management science and engineering, and state coupling constraints happen to be quite natural features in many of these applications. After recalling the results of Rosen (1965) regarding existence and uniqueness of equilibrium of concave game with coupling contraints, we introduce the classical model of Ramsey and presents the Hamiltonian systems approach for its treatment. Next, we extend to a differential game setting the Hamiltonian systems approach and this formalism to the case of coupled state-constraints. Finally, we extend the theory to the case of discounted rewards.


Concave Games Coupling Constraints Differential Games Global Change Game Hamilonian Systems Oligopoly Game Ramsey Model Rosen Equilibrium