# Agent-based models under uncertainty

## TL;DR

This paper compares two methods for handling uncertainty in agent-based models using a battleship simulation, showing that interval methods provide broad results while Monte Carlo methods offer more specific outcomes.

## Contribution

The paper introduces an interval-based approach for epistemic uncertainty in agent-based models and compares it with Monte Carlo methods.

## Key findings

- Interval methods result in many ships with unknown status after many time steps in a highly uncertain environment.
- Monte Carlo simulations tend to conclude with fewer remaining ships after many time steps.
- Interval implementations reveal identities of surviving ships that are nearly mutual with Monte Carlo results but with fewer identities.

## Abstract

Background: Monte Carlo (MC) is often used when trying to assess the consequences of uncertainty in agent-based models (ABMs). However, this approach is not appropriate when the uncertainty is epistemic rather than aleatory, that is, when it represents a lack of knowledge rather than variation. The free-for-all battleship simulation modelled here is inspired by the children’s battleship game, where each battleship is an agent.

Methods: The models contrast an MC implementation against an interval implementation for epistemic uncertainty. In this case, our epistemic uncertainty is in the form of an uncertain radar. In the interval method, the approach occludes the status of the agents (ships) and precludes an analyst from making decisions about them in real-time.

Results: In a highly uncertain environment, after many time steps, there can be many ships remaining whose status is unknown. In contrast, any MC simulation invariably tends to conclude with a small number of the remaining ships after many time steps. Thus, the interval approach misses the quantitative conclusion. However, some quantitative results are generated by the interval implementation, e.g. the identities of the surviving ships, which are revealed to be nearly mutual with the MC implementation, though with fewer identities in total compared to MC.

Conclusions: We have demonstrated that it is possible to implement intervals in an ABM, but the results are broad, which may be useful for generating the overall bounds of the system but do not provide insight on the expected outcomes and trends.