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71 lines
2.5 KiB
Plaintext
71 lines
2.5 KiB
Plaintext
# Thoughts on modelling
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Initial plan is to handle just two operators.
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## Environment
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### Transition function
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#### Debris
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- Currently using a decay formulation for debris.
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- Probably better to use a mass conversion from satellite -> debris
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- This would have to be a stochastic approach to handle satellite destruction.
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- I envision it would be better because it would represent how much debris
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is created better and would easigly lend itself to a size based debris
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approach.
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- It doesn't represent slow degradation well though. It does handle destructive collisions better.
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- Maybe I can ignore satellite on satellite collisions in an initial model because it is the lowest.
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#### Satellite Stocks
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- Probably just fine as is.
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### Market
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- Current plan is to use a cournot market approach with inverse demand: \[ P = a-bQ \]
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- Need to look up dynamic cournot market lit.
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## Operator's Problem
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- Restrict policy to integers (e.g. 1:10)
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- Use a symmetric policy and value function for each operator.
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### Operator State
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- Initally I am going to track one type of debris, the operator's fleet size, and the number of satellites in all other fleets.
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## Social Planner's Problem
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I see two different classes of problems that the Social Planner could face, and both could take various forms.
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Here are the two areas and some variations:
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1. Maximizing long term expected utility/value
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a. Maximize expected value
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b. Preserve value x% of the time
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2. Preserving the resource (manage debris levels)
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a. Keep debris below a threshold.
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b. Keep debris from growing faster than Y rate.
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c. Keep kessler syndrome from occuring in Z% over ZZ periods.
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The first case "should" subsume the second in that minimal debris over a long period should permit more earnings.
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But, if the time-discounting factor is low enough, this might not be the case.
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And this brings up a big issue in that the discount factor of the Social Planner and the Operators might differ
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a lot.
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The question it poses is "Should we use this resource as we best see fit or preserve it for our descendants?"
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## modelling state
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I need to track all constellation sizes and debris size.
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# Thoughts on Interpretation etc,
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One option would be to take derivatives over the value function to get
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Benefit functions. Look at when it is positive etc.
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Another thing to do would be to construct debris tracks.
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Another would be to search for steady states.
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I could compare different versions of the social planner's problem to see
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how they differ, i.e. in debris dynamics etc.
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