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translation of a julia notebook from the discussion around hiding information on the auction endpoint
- surplus draw can be negative; split unsets into a base (forced p_fail) rate and a volatility-driven strategic rate - make the competing solvers' bids explicit as uniform[0, 200] - success-rate / unset terminology; fixed 0-1 success axis, auto c_l range, higher default volatility Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Dashed lines on the optimal-bid panel for the expected routing surplus (1-p_fail)*mu and its value conditional on the routing not failing (mu). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Combine the bid and success-rate plots into a third panel showing the expected value per won auction, V = success*s* - L*(1-success), where the bid s is the surplus delivered to the user and L is the cost of one unset. The optimal cap c_l* is marked on all three panels. - model competing solvers' bid via a configurable density (uniform / triangle / gaussian / rising); keep the reference grid finer than the bid grid so argmax(s*) does not jitter on a flat payoff ridge - normalize the mean surplus to mu = 1 (the model is scale-invariant); the controls are now dimensionless ratios sigma/mu, c_u/mu, L/mu Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
- surplus dropdown switches the routing surplus between the default gaussian and the hardcoded CUSTOM_SURPLUS (value, probability) atoms; mu and sigma are computed from the atoms so the reference lines, the L coupling and the f*sigma cap read the same in both modes - couple the unset cost to volatility, L = (L/sigma) * sigma, and draw a candidate cap c_l = f*sigma (slider f) next to c_l* on every panel Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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This PR adds a notebook with a simple model for solver behavior given caps. The effect of the cap on optimal bids and success rates is visualized.
Example figure:
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