We investigate a generalized Nash equilibrium problem where players are modeled as nodes of network and the utility function each player depends on his/her own action well actions neighbors in network. In case quadratic reference model with shared constraints we able to derive variational solution game series expansion which involves powers adjacency matrix, thus extending previous result. Our ...

The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a “partition function”outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show t...

Generalized Nash games represent an extension of Nash games in which strategy sets are coupled across players. The equilibrium conditions of such a game can be compactly stated as a quasivariational inequality (QVI), an extension of the variational inequality (VI). Harker [9] showed that under certain conditions on the maps defining the QVI, a solution to a related VI solves the QVI. This is a ...

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6], we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we sha...

game theory models decision makers' behaviors in strategic situations. since the structures of games are different, behavior and preferences of the players are different in various types of game. this paper reviews various situations of games. here, characteristics of some common games are discussed and compared. specifically, we focus on a group of games called symmetric games including p...

Real-world planning problems often feature multiple sources of uncertainty, including randomness in outcomes, the presence of adversarial agents, and lack of complete knowledge of the world state. This thesis describes algorithms for four related formal models that can address multiple types of uncertainty: Markov decision processes, MDPs with adversarial costs, extensiveform games, and a new c...

Models and Games by Jouko Väänänen is a book that examines logic from a gametheoretic perspective. Games are nowadays considered to be a standard tool in mathematical logic. They are easy to describe and use and for this reason they have gained wide acceptance in logic during the second half of the twentieth century. Proofs involving games are easier to state and understand and may lead to nove...

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games. Axiomatizations of two classes of generalized values, namely probabilistic generalized values and generalized semivalues, which extend probabilistic values and semivalues, respectively, are firs...

Recently, some significant work has been done to analyze the complexity class of classic electronic games. In these works, the rules of the game are generalized and then the generalized games are classified by formulating them as a decision problem and reducing them to a problem known to be NP-complete [1, 2]. We use a similar approach to prove the complexity class of a particular class of mode...