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Time-Inconsistent Control Theory

Author

Listed:
  • Tomas Björk

    (Stockholm School of Economics)

  • Mariana Khapko

    (University of Toronto)

  • Agatha Murgoci

    (Ørsted)

Abstract

We now go on to study a class of time-inconsistent control problems. Before proceeding to the formal theory, we first recall a part of our discussion on the Bellman optimality principle from the Introduction. We then detail the game-theoretic formulation, whereby we view the problem as a non-cooperative game with one player at each point in time representing different incarnations of decision maker’s preferences. The main result of this chapter is the extension of the standard Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy and the equilibrium value function. We arrive at the extended Bellman system by first studying a couple of simpler problems to highlight the main ideas and then by bringing things together for the general case.

Suggested Citation

Handle: RePEc:spr:sprfcp:978-3-030-81843-2_5
DOI: 10.1007/978-3-030-81843-2_5
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