From optimal control to non-cooperative differential games: A homotopy approach

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Abstract

We propose a new approach to the study of Nash equilibrium solutions to non-cooperative differential games. The original problem is embedded in a one-parameter family of differential games, where the parameter θ € [0,1] accounts for the strength of the second player. When θ= 0, the second player adopts a myopic strategy and the game reduces to an optimal control problem for the first player. As θ becomes strictly positive, Nash equilibrium solutions can be obtained by studying a bifurcation problem for the corresponding system of Hamilton-Jacobi equations.

Original languageEnglish (US)
Pages (from-to)1081-1106
Number of pages26
JournalControl and Cybernetics
Volume38
Issue number4
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Applied Mathematics
  • Modeling and Simulation

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