Sell-side next-offer recommendation. pareto_knob ∈ [0, 1] interpolates between deal-rate-max (0) and H2H-margin-max (1). Returns the recommended offer (in our utility space), acceptance probability, expected payoff, and the inferred posterior over the buyer's WTP.

Buy-side next-offer recommendation with a defense bundle. If anchor_attack_detection is in defenses, supply market_prior {mu, sigma}. Returns recommended offer + warnings + defense actions.

Z-score the opponent's opening offer against a market prior {mu, sigma}. Recommends ignore / counter_with_market / walk_away.

Optimal bid for {first_price | second_price_vickrey | english_ascending}. Vickrey is truthful. First-price uses the BNE for symmetric IPV.

Myerson optimal reserve from virtual-value-equal-seller-valuation.

Recommend format from {first_price, vickrey, english} given weights.

Monte Carlo auction revenue + efficiency.

Stable matching via deferred acceptance. Proposers/receivers each have {id, preferences} (and optional capacity for receivers). Returns a proposer-optimal stable matching plus a blocking-pair sanity check.

Myerson revenue-optimal mechanism for asymmetric IPV. Per-bidder reserves; collapses to second-price-with-reserve under symmetric IPV.

Gallego-van Ryzin posted-price (static p* + dynamic backward-DP schedule).