auction-first-price-shading

Computes the optimal shaded bid for a first-price sealed-bid auction given a true private value, an estimate of the number of competing bidders N, and a value-distribution assumption. Implements the `(N-1)/N` equilibrium shading rule for uniform private values, adjusts for log-normal or empirical value distributions, layers a risk-aversion adjustment, and caps output against the bidder's remaining budget. Domain-neutral auction theory reusable across fantasy sports (baseball FAAB, NBA/NHL waiver auctions), prediction-market limit sizing, sealed procurement bids, and any blind-bid context. Use when user mentions "first-price auction bid", "sealed bid shading", "(N-1)/N", "FAAB bid amount", "auction shading", "optimal bid first-price", "bid for sealed-bid", "blind bid sizing", or when downstream logic needs a principled shade factor rather than an ad-hoc heuristic.