Preprint 2003-069

Semi-cooperative Strategies for Differential Games

Alberto Bressan and Wen Shen

Abstract: The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable.

In the second part of the paper we propose an alternative ``semi-cooperative'' pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.

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Alberto Bressan, <>
Wen Shen, <>
Publishing information:
Also available as SISSA preprint 103-2003-M.
To appear in International Journal of Game Theory.
Submitted by:
<> December 2 2003; updated December 8 2003 and May 4 2004.

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