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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.

Core Idea

A small game (Shubik, 1971) that mechanizes the escalation trap. A prize of fixed value is auctioned, but the second-highest bidder also pays their bid and receives nothing. Backward induction shows why this loser-pays rule spirals: whenever you are second-highest, one more increment converts a certain loss into a possible gain, so each step is locally rational and players escalate past the prize value until one exhausts resources. Its payload is the cut between structural escalation (the rule rewards continuing) and cognitive sunk-cost escalation.

Scope of Application

Lives across the auction-and-mechanism-design subfields of game theory and applied settings that genuinely carry an all-pay contest with a cheap marginal step.

  • All-pay-auction theory — the home turf, the cleanest worked instance of the all-pay family.
  • Patent and pay-to-play litigation — discovery battles where each side's spend is forfeit if it loses.
  • Lobbying and rent-seeking contests — competitions where defeated competitors still forfeit their spend.
  • Conflict studies and arms races — attritional conflicts where the lagging side's investment is wasted unless it presses on.
  • Behavioral economics teaching — the classroom demo in which a small prize auctions for more than its value.

Clarity

Naming the game makes legible a distinction "sunk-cost fallacy" prose collapses: escalation driven by a cognitive error versus escalation driven by an incentive structure that genuinely rewards continuing. Behavior alone cannot separate these. The diagnostic question — reasoning failure to correct, or mechanism to dismantle? — matters because the two species call for opposite remedies.

Manages Complexity

A whole class of protracted escalation episodes reduces to a short structural checklist: a fixed prize, a loser-pays rule, and a cheap marginal step. Where those hold, backward induction delivers the outcome with no case-specific modeling. The two-species cut then collapses diagnosis and remedy to one discriminating question — read the species off the payoff rule, then read the fix off the branch.

Abstract Reasoning

The game licenses a diagnostic detecting the trap from its signature and classifying the species off the payoff rule rather than behavior, an interventionist move breaking the chain by pre-commitment or removing the loser-pays rule (and predicting debiasing fails structurally), boundary-drawing that relocates the rationality from psychology to the rule, and a prediction that clear thinking drives rather than prevents the spiral.

Knowledge Transfer

Within game theory the dollar auction transfers as mechanism — its backward-induction analysis and two remedies carry intact to every setting that literally has the loser-pays/small-step structure (all-pay litigation, rent-seeking, arms races), recognition of the same incentive structure, not analogy. The dividing line beyond auction theory is whether the signature really holds; where it does, the lesson is best carried by the parent escalation_of_commitment under an all-pay incentive. Loose "quagmire" invocations that lack the payoff rule are analogy, sliding back into the cognitive sunk_cost species.

Relationships to Other Abstractions

Local relationship map for Dollar AuctionParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Dollar AuctionDOMAINPrime abstraction: Lock-In — is a decomposition ofLock-InPRIME

Current abstraction Dollar Auction Domain-specific

Parents (1) — more general patterns this builds on

  • Dollar Auction is a decomposition of Lock-In Prime

    Stripping the discrete auction frame leaves a state in which current exposure makes the forward cost of exit exceed one more step of staying.

Hierarchy paths (7) — routes to 4 parentless roots

Neighborhood in Abstraction Space

Dollar Auction sits in a crowded region of the domain-specific corpus (10th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Mechanism Design & Strategic Bargaining (9 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12