We consider a noncooperative game in infinite time horizon, with linear dynamics and exponentially discounted quadratic costs. Assuming that the state space is one-dimensional, we prove that the Nash equilibrium solution in feedback form is stable under nonlinear perturbations. The analysis shows that, in a generic setting, the linear-quadratic game can have either one or infinitely many feedback equilibrium solutions. For each of these, a nearby solution of the perturbed nonlinear game can be constructed.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics