Nonzero-sum differential games

Series Nash solution of two-person, nonzero-sum, linear-quadratic differential games

“…This is identical to the zeroth order term that would be obtained if the imbedding in [4 ] is applied.…”

“…The coefficients ds^/de and ôs^/ôe described above are different from those that would be obtained if the imbedding in [4] were to be applied. The equations resulting from (23) for i = 3,2* are much simpler because e enters linearly in the coefficients of the matrix equations in (8) whereas in the corresponding matrix equations using Starr's imbedding, e would enter nonlinearly.…”

“…o where S^, Q^, iL ^, and are defined in (9), (10) in [4] were to be applied, the imbedded weighting matrices in and would be linear in e but the matrices in the imbedded generalized matrix Riccati equations would have complex dependence on e.…”

“…The use of parameter imbedding for obtaining series solutions for almost zero-sum games has been investigated before [4]. The method in [4] when applied to the linear-quadratic differential game considered in this paper will yield the same zeroth order term in the series as the imbedding method below.…”

“…The method in [4] when applied to the linear-quadratic differential game considered in this paper will yield the same zeroth order term in the series as the imbedding method below. The remaining terms in the series are different for the two imbeddings but the two series will yield the same solution for unity value of the imbedding parameter.…”