The most preferred equilibrium in noncooperative differential games (Q1874847)

Games with a classical Roos-Nash equilibrium can simultaneously admit a state that is not an equilibrium from the classical viewpoint but it is preferred to the classical equilibrium by all players. This state is referred as \(\overline{D}\)-equilibrium. This new notion of equilibrium proves to be actively stable in the sense that, owing to other player's threats, no player would reject it. The author provides an example that a nonzero-sum two person differential game has a unique classical Roos-Nash equilibrium, but the \(\overline{D}\)-equilibrium is preferred by the players. Finally, a method for finding the strongest equilibrium is presented.