Nash Equilibrium of Two Game Models on the Random Social Network

Abstract

It is known that somebody’s behavior (decision) in a stochastic social network may be influenced by that of his (or her) friends. In this paper, we consider two stochastic social network game models (a) and (b) which can be defined respectively by two different utility functions. Some sufficient conditions for the existence of Nash equilibrium (NE) of the two network game models are obtained by analyzing the different effort relation between a player and his (or her) neighbors.