The observation of tolerance in a social network model

In dynamic social networks, agents are able to make and break connections with neighbors to improve their payoffs. Rules have recently developed which help agents evaluate their neighbors and decide whether to break a connection. These rules have introduced the idea of tolerance in dynamic networks by allowing an agent to maintain a relationship with a bad neighbor for some time. In this research, we investigate and define the phenomenon of tolerance in dynamic social networks, particularly with the Highest Rewarding Neighborhood and Highest Weighted Reward rules. We define a mathematical model to predict an agent's tolerance of a bad neighbor and determine the factors that affect it. After defining a general version of tolerance, we explore ideas such as an optimal tolerance and provide situations in which tolerance can be used as a tool to affect network efficiency and network structure. Tolerance of other agents is an intuitive human behavior, and its presence in social network models suggests that the development of social interaction rules among agents shows qualities of human interactions that exist in real life. Introduction Multiagent systems have become increasingly useful in the modeling of social networks, and a recent development in the study of social networks has been the simulation of dynamic social networks, in which agents can choose break off connections or make new connections throughout the course of the simulation. In dynamic social networks, several social interaction rules have been developed to improve agents' decision-making processes so that they break off connections with agents that are not beneficial. In these social network models, some degree of tolerance between agents has been noticed. That is, using some social interaction rules, an agent may not break off a connection with a harmful neighbor. We define tolerance as such: Definition 1: Tolerance is the description of an agent's willingness to maintain an unstable connection with some other agent. Definition 2: We call an agent that chooses to maintain an unstable connection for n turns n-tolerant. Definition 3: We define a stable connection as a connection which, given that nothing changes, will never be broken. The primary goal of this study is to develop a full understanding of tolerance in social networks and its effects. We will first provide models to predict tolerance in several social networks. Once these have been established and confirmed, our goal will be to develop further conclusions about tolerance in social networks: we will compare the developed models and study the effects of tolerance in social networks to develop an understanding of how control of tolerance in a dynamic network can be used. Tolerance is a concept intuitively present in real social networks, and by studying the causes and effects of tolerance in social network models, it can be consciously used in the development of new social interaction rules, rather than simply being a side effect of many rules with no determined cause.