Auctions, Revelation & Strategic Pricing

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Abstractions about auction formats, truthful revelation, revenue equivalence, strategic bidding, holdouts, and paradoxes of competitive price formation.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Bertrand Paradox (Economics) — Compute the extreme corner of price competition — two firms selling an identical good at equal marginal cost price at marginal cost with zero profit — as a deliberately-wrong baseline whose gap to real margins becomes a five-assumption diagnostic audit.
• Dollar Auction — Mechanize the escalation trap with one rule change — the second-highest bidder also pays and gets nothing — so that backward induction makes each additional bid locally rational and rational players escalate past the prize's value.
• Edgeworth Paradox — Show that Bertrand's price-equals-marginal-cost result collapses once firms face capacity constraints below total demand: no pure-strategy equilibrium exists and prices cycle endlessly between the competitive floor and monopoly ceiling.
• Holdout Problem — The bargaining failure in which a complementary surplus requiring unanimous consent lets any pivotal, non-substitutable party refuse agreement and extract a disproportionate share as the price of consent — making rational extraction, not bad faith, the equilibrium.
• Revelation Principle — The mechanism-design theorem that any outcome achievable by any mechanism is also achievable by a direct mechanism where agents truthfully report their private type — collapsing the search over all mechanisms to a tractable optimization over incentive-compatibility constraints, while saying nothing about which mechanism to deploy.
• Revenue Equivalence Theorem — The auction-theory result that under symmetric independent-private-values conditions, every format allocating to the highest bidder yields the seller the same expected revenue — pinning revenue to the allocation rule and lowest-type rent, so format matters only where a condition fails and the failure direction names the preferred format.
• Vickrey Auction — A sealed-bid auction where the highest bidder wins but pays the second-highest bid, decoupling what you win from what you pay so that bidding your true valuation is the dominant strategy — no rival-modeling needed — and the item reaches whoever values it most.