Optim Lett (2018) 12:375–386
A Stackelberg differential game for defence and
Received: 27 August 2016 / Accepted: 5 September 2017 / Published online: 26 September 2017
© Springer-Verlag GmbH Germany 2017
Abstract We considered counterterror measures and the economic growth Stack-
elberg differential game. The equilibrium of this game was acquired by using the
Maximal Principle. We also characterized the optimal strategy for the government and
terrorist organization and compared it with Nash equilibrium published previously.
Keywords Stackelberg differential games · Optimal strategy ·
Recently, as terrorist attacks become increasingly rampant, “terrorism” has received
extensive attention from various research ﬁelds. Great efforts in social investigation,
statistical analysis and mathematical proof have been devoted to ﬁnding out resolu-
tions to terrorism. Owing to the intense rivalry between governments and terrorist
organizations, the theory of optimal control and the game theory are commonly used
to build relevant models [3–10].
Most studies target at the systems about the game of terrorist organization resource
x(t), or namely only one dynamic equation.
˙x = h(u,v)
School of Basic Science, Changchun University of Technology, Changchun 130012,
People’s Republic of China