Simulating Tolerance in Dynamic Social Networks

Introduction

In multi-agent systems, different agents aim to achieve different goals, yet must develop some system of cooperation within the system (Axelrod, 1997; Davidsson, 2002). In this research, the systems of social networks (Epstein, 1999; Watts, 1999; Newman, 2003) are of particular interest to us. In such systems, all agents are self-interested and try to maximize their own utility. This can be done by adjusting their strategy or by adjusting their environment and disconnecting from agents while making connections with others. These systems can be governed by pre-determined rules to control individual decision making and social interactions. The existence of a basic network model, such as random network, small-world network (Watts, 1999), and scale free network (Newman, 2003), couple with some economic game, provides a network of self-interested agents with specific goals, and the application of individual decision making rules and social interaction rules make the network dynamic, resulting in questions about the final network structure, such as stability, efficiency, and tolerance.

The current research in this direction occurs on two different levels: a low-level decision that an agent must make to determine its game strategy, and a higher-level decision to change the links in the network, and, ultimately, the overall network structure. Most of the current research uses the static network so only the low-level decision is achieved, i.e. the agents can only change their own actions but not other agents that they are connected to. Here a network will be called static if edges are never created or removed after the generation of the graph. Static networks may well model social behaviors in a relative stable environment such as a community where people barely move around and always keep the same relationships to others.

Our research focuses on dynamic networks that the edges are created and removed as the network evolves. Therefore in our system, both the low-level decision on agent’s individual actions and higher-level decision on agent’s social interactions are considered to help agents maximize their utility. The dynamic network approach can model many dynamic systems such as behaviors in social network service (SNS) where agents frequently change their relationships to others. Examples include the friendship networks of high school students (Fararo & Sunshine, 1964), the network of citations between scientific papers (Redner, 1998), links between web pages on the World Wide Web (Albert & Barb'asi, 2002) and network of human sexual contact (Liljeros, Edling, Amaral, Stanely, & Aberg, 2001).

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. One of these social interaction rules is called the Highest Weighted Reward (HWR) in order to give agents the ability to update their neighborhood in a social network (Wu & Zhang, 2009). The HWR rule weighted recent rewards from a relation more than that of the long-time-ago rewards. Agents’ decision about whether to keep a relationship or not is based on if the weighted rewards is greater than the weighted average reward earned from every relationship. Adopting the HWR rule, one can easily transform a classic static network into a dynamic network with few restrictions on how agents observe their neighbors and how agents make the decision about when to keep an existing connection or disconnect it so they can connect to a new neighbor. A special case of the HWR rule is when the weight is 1 so all previous interactions are weighted as the same in agent’s current decision. We call this special case another rule – the HRN rule (Highest Rewarding Neighborhood) (Zhang & Leezer, 2009).