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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show all references

References:
[1]

Wiley, New York, 1984.  Google Scholar

[2]

J. Math. Contr. Sign. Syst., 25 (2013), 311-326. doi: 10.1007/s00498-012-0105-z.  Google Scholar

[3]

Stochastics, 8 (1983), 297-323. doi: 10.1080/17442508308833244.  Google Scholar

[4]

Stochastics, 20 (1987), 121-150. doi: 10.1080/17442508708833440.  Google Scholar

[5]

Appl. Math. Optim., 13 (1985), 259-282. doi: 10.1007/BF01442211.  Google Scholar

[6]

J. Indiana Univ. Math., 27 (1978), 143-157. doi: 10.1512/iumj.1978.27.27012.  Google Scholar

[7]

Vol. 2, Academic Press, 1976.  Google Scholar

[8]

Proc. Amer. Math. Soc., 3 (1952), 170-174.  Google Scholar

[9]

J. Diff. Equ., 37 (1980), 108-139. doi: 10.1016/0022-0396(80)90092-3.  Google Scholar

[10]

Israel J. Math., 40 (1981), 165-174. doi: 10.1007/BF02761907.  Google Scholar

[11]

Ann. Probab., 19 (1991), 538-561. doi: 10.1214/aop/1176990440.  Google Scholar

[12]

Russian Math. Surveys, 25 (1970), 3-55.  Google Scholar

[13]

Theo. Prob. Appl., 20 (1976), 599-602. doi: 10.1137/1120064.  Google Scholar

[14]

Theo. Prob. Appl., 21 (1977), 817-821. doi: 10.1137/1121030.  Google Scholar

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