In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...

We study basic properties of a class of noncooperative games whose players are selfish, distributed users of a network and the game’s broad objective is to optimize Quality of Service (QoS) provision. This class of games was previously introduced by the authors and is a generalization of well-studied network congestion games. The overall goal is to determine a minimal set of static game rules b...

We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ord...

We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley-Clifford theorem, it follows that the potentials of such games can be decomposed to l...

The recent theory of sequential games and selection functions by Escardó & Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalized to games defined by selection functions. A normal form construction is given, which generalizes the game-theoretic normal form, and its soundness is proved. Minimax stra...

In this paper, the generalized forms of the fuzzy core and the Shapley function for dynamic fuzzy games on matroids are given. An equivalent form of the fuzzy core is researched. In order to better understand the fuzzy core and the Shapley function for dynamic fuzzy games on matroids, we pay more attention to study three kinds of dynamic fuzzy games on matroids, which are named as fuzzy games w...

Generalized notions of potential maximizer, monotone potential maximizer (MP-maximizer) and local potential maximizer (LPmaximizer), are studied. It is known that 2 × 2 coordination games generically have a potential maximizer, while symmetric 4 × 4 supermodular games may have no MPor LP-maximizer. This note considers the case inbetween, namely the class of (generic) symmetric 3 × 3 supermodula...

In this paper, a generalized form of the Banzhaf-Owen value for cooperative fuzzy games with a coalition structure is proposed. Its axiomatic system is given by extending crisp case. In order to better understand the Banzhaf-Owen value for fuzzy games with a coalition structure, we briefly introduce the Banzhaf-Owen values for two special kinds of fuzzy games with a coalition structure, and giv...

The mechanism by Hart and Mas-Colell (1996) for non-transferable utility (NTU) games is generalized so that a coalition structure among players is taken into account. The new mechanism yields the Owen value for transferable utility (TU) games with coalition structure as well as the consistent value (Maschler and Owen 1989, 1992) for NTU games with trivial coalition structure. Furthermore, we ob...

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...