# American Institute of Mathematical Sciences

January  2015, 2(1): 51-63. doi: 10.3934/jdg.2015.2.51

## On noncooperative $n$-player principal eigenvalue games

 1 Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, United States, United States

Received  November 2014 Revised  February 2015 Published  June 2015

We consider a noncooperative $n$-player principal eigenvalue game which is associated with an infinitesimal generator of a stochastically perturbed multi-channel dynamical system -- where, in the course of such a game, each player attempts to minimize the asymptotic rate with which the controlled state trajectory of the system exits from a given bounded open domain. In particular, we show the existence of a Nash-equilibrium point (i.e., an $n$-tuple of equilibrium linear feedback operators) in a game-theoretic setting that is connected to a maximum closed invariant set of the corresponding deterministic multi-channel dynamical system, when the latter is composed with this $n$-tuple of equilibrium linear feedback operators.
Citation: Getachew K. Befekadu, Panos J. Antsaklis. On noncooperative $n$-player principal eigenvalue games. Journal of Dynamics & Games, 2015, 2 (1) : 51-63. doi: 10.3934/jdg.2015.2.51
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