Wen Shen
SISSA
Small BV Solutions of Hyperbolic Non-cooperative Differential Games
This is a joint work with Alberto Bressan.
The talk will begin with a brief introduction to non-cooperative
differential game, which is actually an optimal control problem.
I will formally derive the Hamilton Jacobian equations
and the corresponding system of conservation laws.
The hyperbolicity of the system is essential,
and neccesary conditions are derived.
In the positive case, the weak solution of the system of conservation
laws determines an n-tuple of feedback strategies.
These yield Nash equilibrium solutions to the non-cooperative
differential game.
Some discussion about extensions and future work will be given at the
end of the talk, where we will also discuss partially cooperative
strategies which always yield a hyperbolic system.
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