Abstract
In this note, we consider a special class of continuous-time two-person two-criteria decision-making problems characterized by linear descriptor systems and quadratic cost functionals. We show that there exists an equilibrium solution which minimizes two different cost functionals simultaneously. Therefore, such an equilibrium solution can be interpreted as either a Nash equilibrium solution in the noncooperative mode of decision making or a Pareto-optimal solution in the cooperative mode of decision making. The equilibrium solution obtained is in linear feedback form. It seems that there exist no counterpart solution for the same problem of state space systems.
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Communicated by G. Leitmann
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Xu, H., Mizukami, K. Two-person two-criteria decision making problems for descriptor systems. J Optim Theory Appl 78, 163–173 (1993). https://doi.org/10.1007/BF00940706
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DOI: https://doi.org/10.1007/BF00940706