Subgame Perfect Nash Equilibrium as solution of a control problem
The computation of Nash equilibrium in differential games is a difficult task, due to the interactions in the players' strategies. A class of games, known as Potential Games, has the feature that the open loop Nash equilibrium is the solution of a suitable single-player control problem. This facilitates the analysis of the equilibrium and allow to use standard techniques of Control Theory to prove existence and to characterize the solution. Unfortunately, strategies based on open loop rules are most often not temporally consistent, in the sense that they prescribe suboptimal solutions at intermediate stages of the game. Feedback rules prevent this difficulty. To our knowledge, the problem of characterizing Subgame Perfect Nash Equilibrium as the solution of a control problem has not been addressed in the literature. We develop in this paper a method for doing this and show its applicability in a problem arising in economics.
Palabras clave / Keywords: subgame perfect nash equilibrium differential games potential games
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