TY - JOUR
T1 - Bifurcation analysis of a non-cooperative differential game with one weak player
AU - Bressan, Alberto
N1 - Funding Information:
This research was partially supported by NSF, with grant DMS-0807420. The paper was written as part of the international research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2008–2009.
PY - 2010/3/15
Y1 - 2010/3/15
N2 - We study a bifurcation problem for a system of two differential equations in implicit form. For each value of the parameter θ, the solution yields a pair of Nash equilibrium strategies in feedback form, for a non-cooperative differential game. When θ = 0, the second player has no power to influence the dynamics of the system, and his optimal strategy is myopic. The game thus reduces to an optimal control problem for the first player. By studying the bifurcation in the solutions to the corresponding system of Hamilton-Jacobi equations, one can establish existence and multiplicity of solutions to the differential game, as θ becomes strictly positive.
AB - We study a bifurcation problem for a system of two differential equations in implicit form. For each value of the parameter θ, the solution yields a pair of Nash equilibrium strategies in feedback form, for a non-cooperative differential game. When θ = 0, the second player has no power to influence the dynamics of the system, and his optimal strategy is myopic. The game thus reduces to an optimal control problem for the first player. By studying the bifurcation in the solutions to the corresponding system of Hamilton-Jacobi equations, one can establish existence and multiplicity of solutions to the differential game, as θ becomes strictly positive.
UR - http://www.scopus.com/inward/record.url?scp=75249100657&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=75249100657&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2009.11.025
DO - 10.1016/j.jde.2009.11.025
M3 - Article
AN - SCOPUS:75249100657
SN - 0022-0396
VL - 248
SP - 1297
EP - 1314
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 6
ER -