# Wolfram Summer SchoolFounded in 2003

17th Annual Wolfram Summer School, held at Bentley University June 23–July 12, 2019

Alumni

# Han Fu

Class of 2014

## Bio

Han is an undergraduate student at Beijing Normal University, majoring in management science. She has established several agent-based models to study socioeconomic issues, including how fair offers emerge in the ultimatum game, and how aggregation arises from a mutually beneficial interaction. She is now interested in building macroeconomic models to explore the impacts of debt on the economy. In her recent work, she has investigated the processes of money creation and money circulation in a credit economy. After undergrad, she will probably continue her research on macroeconomics with her current mentor.

## Project: Emergence of Aggregation from an Agent-Based Model

An agent-based model is studied in this project, where agents are distributed on a line and seek for their best positions through adaptive learning. The movements of agents are driven by benefits obtained from those with higher status, and restricted by their initial positions. The benefit gained by agent i from agent j at time t is formulated as follows:

where x represents the current positions of agents, and Subscript[x, i](0) is the initial position of agent i. Then the expected benefit of agent i is given by:

Whether the agent moves forward, backward, or doesn't move at all depends on which option could bring him the largest benefit.

What fascinates me most is that a model with such simple rules could produce some complex patterns, similar to cellular automata. Aggregations of agents will emerge in the form of clusters when we record the distribution of agents along the position line. While the agents attempt to move upward, the clusters will shift downward and collapse almost at a fixed point. Even if the pace lengths of agents are fixed, which means the only randomness existing in the model is the initial positions of agents, the complex aggregation pattern will still appear.

In this project, I analyze some basic statistical properties of the output of the model, such as the distribution of the duration times of clusters, the speed at which they shift, and the position where they collapse. To be more generalized, I modify the model by introducing a parameter into the benefit function and changing the distribution of agents' pace lengths. The combined impact of the parameter in the benefit function and the standard deviation of pace lengths on the entropy of the system is examined.

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