Incorporating recursive numeral systems into the agents' learning process would introduce a new level of complexity and flexibility in their communication strategies. Recursive systems, unlike exact and approximate systems, allow for the representation of an infinite range of numbers through a recursive structure. This means that the agents would need to learn not only to convey specific numbers but also to understand and generate numerical expressions that can represent any magnitude.
The introduction of recursive systems would require the agents to develop a deeper understanding of numerical concepts and relationships. They would need to learn how to recursively combine basic numeral words to express larger quantities, which adds a layer of abstraction and complexity to their communication. This would involve learning not only the mapping between individual words and numbers but also the rules for combining these words to represent more complex numerical values.
In terms of the results, allowing the agents to develop recursive numeral systems could lead to more sophisticated and expressive communication capabilities. The agents would be able to convey a wider range of numerical values with greater precision and flexibility. However, this increased complexity may also pose challenges in terms of learning and convergence. The agents would need to navigate a more intricate search space to find optimal communication strategies, which could potentially require more training data and computational resources.