Search

This study is concerned with the stability of Nash equilibria for a class of nn-person noncooperative differential games. More precisely, due to a preorder induced by a convex cone on a real linear normed space, we define a new concept called ordering stability of equilibria against the perturbation of the right-hand side functions of state equations for the differential game. Moreover, using the set-valued analysis theory, we present the sufficient conditions of the ordering stability for such differential games.

In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space. [ABSTRACT FROM AUTHOR]

In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results. [ABSTRACT FROM AUTHOR]

We study a twice-repeated pricing game in the quantum domain. Two firms play this game, and both firms have three pricing strategies. The classical version of the repeated game has multiple Nash equilibria in every stage. We prove that the classical version of this twice-repeated game is a subset of the quantum game. We find that if the initial state is prepared to be entangled, then under certain conditions, there are three pure-strategy Nash equilibria in every stage of the game, and both firms can obtain higher payoffs than they can in the corresponding classical game. [ABSTRACT FROM AUTHOR]

This paper presents sufficient conditions for the existence of solutions to nonlinear impulsive Volterra integral inclusions and initial value problems for second order impulsive functional differential inclusions in Banach spaces. Our results are obtained via a fixed point theorem due to Hong [J. Math. Anal. Appl. 282 (2003) 151–162] for discontinuous multivalued increasing operators. [Copyright &y& Elsevier]