Hi! Any thoughts on how to simplify this expression or rewrite it?
Pr(Y_ij≥Y_ik+b_j−b_k ∀k)−Pr(Y_ij≥Y_ik ∀k) ?
I want to keep things as general as possible.
Y_ij is the outcome if entity i chooses action j, Y_ik is the outcome if entity i choose action k
b_j is the cost of doing j, b_k is the cost of choosing action k
These are discrete random variables. For illustrative purposes, can suppose k ranges from 1-10 i.e. 10 different actions to choose from.
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