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