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Infinite Horizon Concave Games with Coupled Constraints

In: Handbook of Dynamic Game Theory

Author

Listed:
  • Dean Carlson

    (American Mathematical Society, Mathematical Reviews)

  • Alain Haurie

    (ORDECSYS and University of Geneva
    GERAD-HEC Montréal PQ)

  • Georges Zaccour

    (GERAD, HEC Montréal, Department of Decision Sciences)

Abstract

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.

Suggested Citation

  • Dean Carlson & Alain Haurie & Georges Zaccour, 2018. "Infinite Horizon Concave Games with Coupled Constraints," Springer Books, in: Tamer Başar & Georges Zaccour (ed.), Handbook of Dynamic Game Theory, chapter 3, pages 111-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44374-4_34
    DOI: 10.1007/978-3-319-44374-4_34
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