On noncooperative $n$-player principal eigenvalue games

Getachew K.  Befekadu; Panos J.  Antsaklis

doi:10.3934/jdg.2015.2.51

Article Contents

2015, Volume 2, Issue 1: 51-63. Doi: 10.3934/jdg.2015.2.51

This issue Previous Article Hamiltonian evolutionary games Next Article Discrete time dynamic oligopolies with adjustment constraints

On noncooperative $n$-player principal eigenvalue games

Getachew K. Befekadu^1, and
Panos J. Antsaklis^1,

1.
Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556

Received: November 2014

Revised: February 2015

Published: January 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 34D10, 34D20, 47H10, 91A10, 93B60.

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