Studying Exploitation Dynamics using Differential Game Theory

Studying Exploitation Dynamics using Differential Game Theory

Summary: Utilizing differential game theory, this project seeks to model the exploitative dynamics between powerful and weaker groups, revealing optimal strategies for minimizing exploitation and asserting effective retaliatory measures.

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

Source of Idea:
Was thinking about bullying, the Russia-Ukraine war whilst I was in a Differential Game Theory research group. Turned out to be a great intersection to explore.
Skills Needed to Execute This Idea:
Differential Game TheoryMathematical ModelingOptimization AlgorithmsData AnalysisCase Study EvaluationStrategic PlanningResearch MethodologyStatistical AnalysisEconomic TheoryGame TheoryDocumentation SkillsCritical ThinkingSimulation TechniquesInterdisciplinary Collaboration
Categories:ResearchMathDifferential Game TheoryPolitical Science

Hours To Execute (basic)

200 hours to execute minimal version ()

Hours to Execute (full)

250 hours to execute full idea ()

Estd No of Collaborators

1-10 Collaborators ()

Financial Potential

$0–1M Potential ()

Impact Breadth

Affects 100K-10M people ()

Impact Depth

Significant Impact ()

Impact Positivity

Maybe Helpful ()

Impact Duration

Impacts Lasts Decades/Generations ()

Uniqueness

Moderately Unique ()

Implementability

Very Difficult to Implement ()

Plausibility

Reasonably Sound ()

Replicability

Moderately Difficult to Replicate ()

Market Timing

Good Timing ()

Project Type

Research

Project idea submitted by u/itgetsbetter.
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