The notion of Berge equilibrium is a generalization of Nash equilibrium, which has its theoretical basis in fixed point theorems. We point out parallel but novel results for the Berge theory and also show many illustrative examples. Some relation to the prisoners' dilemma is shown as well. The results here generalize those of Radjef and the authors. © 2004 Elsevier Inc. All rights reserved.

In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in [8], we prove an existence theorem. As an application, we study the repeated extended Bertrant duopoly model of price competition.

in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

This paper investigates the stability analysis of fuzzy relational dynamic systems. A new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. This approach is also investigated for other types of fuzzy relational composit...

In this paper, we have analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations. We gain some conditions for global stability of trivial and interior equilibrium point.

It is often demonstrated that Brouwer’s fixed point theorem can not be constructively proved. Therefore, Kakutani’s fixed point theorem, the Fan-Glicksberg fixed point theorem and the existence of a pure strategy Nash equilibrium in a strategic game with continuous (infinite) strategies and quasi-concave payoff functions also can not be constructively proved. On the other hand, however, Sperner...

As a continuation of previous work of the first author with S. Ranjbar [26] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudomon...

We propose two simple controls for the regulation of an under actuated rotational pendulum. Both controllers are based on the Lyapunov approach; the first is a simple passive control which makes the closed-loop solution converges asymptotically to an equilibrium manifold. The second approach is a combination of the Lyapunov and the off-line trajectory planning approaches to move the pendulum fr...

We propose two simple controls for the regulation of an under actuated rotational pendulum. Both controllers are based on the Lyapunov approach; the first is a simple passive control which makes the closed-loop solution converges asymptotically to an equilibrium manifold. The second approach is a combination of the Lyapunov and the off-line trajectory planning approaches to move the pendulum fr...

A game-theoretic model is presented to study the management of transmission power in a wireless data network. We propose a power game for a multiuser multicarrier setting where all the users are assumed to transmit at equal rate. At equilibrium, each user is shown to transmit over a single carrier, as in [Mehskati et al., 2006]. We derive the necessary conditions on the path gains when the Nash...