Abstract
The authors study the Nash equilibria of a class of two-person nonlinear, deterministic differential games where the players are weakly coupled through the state equation and their objective functionals. The weak coupling is characterized in terms of a small perturbation parameter ε. With ε = 0, the problem decomposes into two dependent standard optimal control problems, while for ε ≠ 0, even though it is possible to derive the necessary and sufficient conditions to be satisfied by a Nash equilibrium solution, it is not always possible to construct such a solution. An iterative scheme is developed to obtain an approximate Nash solution when ε lies in a small interval around zero. Further, after requiring strong time consistency of the Nash equilibrium solution when at least one of the players uses dynamic information, the issue of existence and uniqueness of these solutions is studied for the cases when both players use the same information, either closed-loop or open-loop. It is also shown that even though the original problem is nonlinear, the higher (than zero'th) order terms in the Nash equilibria can be obtained as solutions to LQ (linear quadratic) optimal control problems, or static quadratic optimization problems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 252-257 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 1 |
| State | Published - Dec 1 1990 |
| Event | Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: Dec 5 1990 → Dec 7 1990 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Cite this
Iterative computation of noncooperative equilibria in nonzero-sum differential games with weakly coupled players. / Srikant, Rayadurgam; Basar, M Tamer.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 1, 01.12.1990, p. 252-257.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Iterative computation of noncooperative equilibria in nonzero-sum differential games with weakly coupled players
AU - Srikant, Rayadurgam
AU - Basar, M Tamer
PY - 1990/12/1
Y1 - 1990/12/1
N2 - The authors study the Nash equilibria of a class of two-person nonlinear, deterministic differential games where the players are weakly coupled through the state equation and their objective functionals. The weak coupling is characterized in terms of a small perturbation parameter ε. With ε = 0, the problem decomposes into two dependent standard optimal control problems, while for ε ≠ 0, even though it is possible to derive the necessary and sufficient conditions to be satisfied by a Nash equilibrium solution, it is not always possible to construct such a solution. An iterative scheme is developed to obtain an approximate Nash solution when ε lies in a small interval around zero. Further, after requiring strong time consistency of the Nash equilibrium solution when at least one of the players uses dynamic information, the issue of existence and uniqueness of these solutions is studied for the cases when both players use the same information, either closed-loop or open-loop. It is also shown that even though the original problem is nonlinear, the higher (than zero'th) order terms in the Nash equilibria can be obtained as solutions to LQ (linear quadratic) optimal control problems, or static quadratic optimization problems.
AB - The authors study the Nash equilibria of a class of two-person nonlinear, deterministic differential games where the players are weakly coupled through the state equation and their objective functionals. The weak coupling is characterized in terms of a small perturbation parameter ε. With ε = 0, the problem decomposes into two dependent standard optimal control problems, while for ε ≠ 0, even though it is possible to derive the necessary and sufficient conditions to be satisfied by a Nash equilibrium solution, it is not always possible to construct such a solution. An iterative scheme is developed to obtain an approximate Nash solution when ε lies in a small interval around zero. Further, after requiring strong time consistency of the Nash equilibrium solution when at least one of the players uses dynamic information, the issue of existence and uniqueness of these solutions is studied for the cases when both players use the same information, either closed-loop or open-loop. It is also shown that even though the original problem is nonlinear, the higher (than zero'th) order terms in the Nash equilibria can be obtained as solutions to LQ (linear quadratic) optimal control problems, or static quadratic optimization problems.
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UR - http://www.scopus.com/inward/citedby.url?scp=0025538150&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:0025538150
VL - 1
SP - 252
EP - 257
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
ER -