Powerful groups often exploit weaker groups for their own economic benefit (eg: slavery, bullying, colonialism etc). However, if this exploitation becomes excessive, the powerful group becomes subject to retaliation by the weaker group and/or third parties and thus faces substantial economic damage. As a result, the powerful groups usually vary how exploitative or altruistic they are towards the weaker group over time in order to maximise their own net economic gains. For example, one approach is to be consistently somewhat exploitative; another might be to exploit a lot initially, then become extremely altruistic.

I had previously attempted to mathematically model this dynamic using differential game theory. The goal was to create a general model, for which appropriate parameters can be chosen depending on the situation. Then the optimization algorithm should tell us what the best way for the invovled parties (stronger group, weaker group and third parties) is in order to maximise their individual payoffs. This model can then be evaluated using case studies from the past. The goal was to analyze the results from various different scenarios in order to construct general principles which the weaker group could use in order to minimize the amount of exploitation they face. Possibly also rate the effectiveness of different kinds of retaliation strategies.

However, due to time constraints, a lack of career alignment and a lack of expertise, I haven’t been able to complete this project. I don’t see myself doing it either. My work so far can be found at https://drive.google.com/drive/folders/1NE4Rn2OIrFRBF8SiP9Ee9UL3fwQNEQ3i?usp=sharing

If it sounds interesting, I’d love it if someone can turn it into a proper publishable paper. I don’t require that you formally credit me for anything, but if you insist, a mention in the acknowledgement section of the paper should suffice.

I found these two documents to be helpful in learning about Differential Game Theory: https://math.berkeley.edu/~evans/control.course.pdf and https://math.berkeley.edu/~evans/math 195 notes.pdf