The Generic Uniqueness and Well-Posedness of NashEquilibria for Stable Population Games

This paper aims at studying a new kind of stable population games introduced by J.Hofbauer and H.Sandholm in 2009.We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem.It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium.Then,we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.