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...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.展开更多
Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Na...Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.展开更多
基金This work was supported by the National Natural Science Foundation of China(No.11561013)the Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China(No.[2015]192)+1 种基金the Joint Foundation of Guizhou Province and Guizhou University(Nos.QKH[2014]7643,QKH[2016]7425)the Introduced Talent Foundation of Guizhou University(Nos.[2014]05,[2018]11).
文摘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.
基金supported by Consejo Nacional de Ciencia y Tecnología of Mexico (Grant No. 221291)
文摘Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.
