Multi-Agent Model of Innovation in a Competitive Environment

Overview

This project simulates the evolution of multiple innovators (e.g., research groups) in a competitive environment, such as the Boston research landscape. Each agent evolves its innovation and competition levels over time, influencing its overall fitness, according to a system of differential equations.

Mathematical model

The model is governed by the following system of differential equations for each agent:

$$ \frac{dI_i(t)}{dt} = r_{I,i} \cdot I_i(t) \cdot (1 - \delta \cdot C_i(t)) $$

$$ \frac{dC_i(t)}{dt} = r_{C,i} \cdot C_i(t) \cdot \left(\gamma \cdot F_i(t) - \frac{I_i(t)}{I_i(t) + 1}\right) $$

$$ \frac{dF_i(t)}{dt} = \alpha \cdot I_i(t) - \beta \cdot C_i(t) $$

Where:

• I_i(t): Innovation level of agent i at time t.
• C_i(t): Competition level of agent i at time t.
• F_i(t): Fitness level of agent i at time t.
• r_I,i: Innovation growth rate for agent i.
• r_C,i: Competition growth rate for agent i.
• α, β, γ, δ: Constants representing interactions between innovation, competition, and fitness.

Agents

Innovator Class

Each innovator (e.g. a research group) is modeled as an agent with the following attributes:

• Innovation: Represents the innovator's capacity for developing new ideas.
• Competition: Represents the pressure the innovator faces from other innovators.
• Fitness: Calculated based on innovation and competition.

Key Methods

• innovate(): Updates the innovation level according to the differential equation.
• compete(): Updates the competition level according to the differential equation.
• updateFitness(): Updates fitness based on innovation and competition.
• passTime(): Simulates the passage of one time step.

Environment

CompetitiveEnvironment Class

Manages the interactions between multiple research groups:

• simulate(): Runs the simulation over multiple time steps, updating the state of each innovator.
• logState(): Logs the state of all innovator at each time step.

Running the Simulation

To run the simulation:

1. Compile:

javac src/*.java

2. Run:

java -cp src CompetitiveEnvironment

3. Plot the results in the jupyter notebook plot.ipynb. Make sure to adapt the file path of the .csv file containing simulation results.