The Game-Change Theorem

LIBOR shows why fines can leave the game intact

The paper starts from the 2012 LIBOR manipulation case: a benchmark used in $350 trillion in financial contracts was built on panel-bank submissions, so the inherited information structure rewarded self-serving reports.

• Regulators imposed more than $9 billion in fines, but the benchmark was not repaired by punishment alone.
• The paper treats LIBOR as an information-architecture failure: dealer submissions were the wrong object to observe.
• The repair was rule transformation: replacing LIBOR with SOFR shifted the benchmark toward transaction observation.

The theorem applies only when system welfare is missing from the inherited game

The Game-Change Theorem is the companion to the Missing System Theorem. It applies when the inherited game satisfies Partial Overlap, Non-Observability, and Discount Rate Asymmetry.

• MST premise: system welfare W lies outside the payoff space, with ∂Ui/∂W = 0 for all agents i.
• System-Omission Tension means privately efficient play can degrade the shared system condition.
• The paper rejects using “change the game” as a slogan; the analyst must name G, the bad equilibrium, the within-game failure, and the transformation class.

A Hollow Win is private gain with system loss

The paper uses the MST eight-outcome taxonomy to isolate the failure mode. In a Hollow Win, both private sides improve while the system condition worsens.

• Formal condition: s* ∈ E(G), Ui(s*) > Ui(s0) for all i, and W(s*) < W(s0).
• LIBOR fits the pattern: panel banks could benefit from submissions while benchmark trust degraded.
• The problem is not low penalties alone; W is non-derivable from the payoff and observation records inside G.

A liability transformation can eliminate the Hollow Win

1 gives a constructive existence proof: for every MST game G, there is a transformed game G′ in which the Hollow Win is eliminated and W is recoverable from the payoff structure.

• The transformation adds λi(W), a liability function tied to system-welfare loss.
• Construction: λi(W) = αi · max 0, W(s0) − W(s) , with αi > Ui(s*) − Ui(s0).
• At s*, the transformed payoff falls below the threat-point payoff, so s* cannot remain an equilibrium in G′.

Mechanism design cannot approximate the transformation optimum

The paper argues that mechanisms inside G remain informationally closed. They can alter prices, reports, audits, and sanctions, but they cannot condition on a welfare object the game never records.

• M(G) is a proper subset of the outcomes reachable through game transformation G(G).
• No sequence of Pigouvian taxes, subsidies, or disclosure duties converges to the game-transformation optimum.
• Examples in the paper: disclosure leaves platform self-preferencing intact; fines leave a submission-based benchmark intact; carbon reporting without border liability leaves leakage attractive.

Optimal transformation search is NP-hard, so the target is satisficing

The decision problem GAME-TRANSFORM is NP-complete by reduction from Minimum Dominating Set. The paper uses that boundary to replace exact optimization with a dominance test against the status quo.

• For games with N ≥ 10, no polynomial-time exact algorithm exists unless P = NP.
• The policy question becomes: which transformation is good enough to dominate the inherited game?
• The paper’s standard is not full welfare maximization; it is a reconstructable transformation that improves on G and targets the component causing the Hollow Win.

Every welfare-improving rule change fits one primitive operation

Proposition 12 states that welfare-improving transformations decompose into three primitive operations, complete up to isomorphism.

• R1 liability shift: change payoffs by assigning the system cost to the actor that creates it.
• R2 strategy constraint: change the strategy set by prohibiting the welfare-destroying move.
• R3 information architecture: change what is observed, recorded, and reconstructable.
• Dominant-class test: remove the primitive; if the Hollow Win returns, that primitive is doing the work.

The three institutional witnesses map cleanly to R3, R2, and R1

The cases are not randomized evidence of welfare maximization. The paper uses them as institutional witnesses for the three transformation classes.

• LIBOR→SOFR is R3: it replaces self-reported estimates with transaction-based benchmark construction.
• EU Digital Markets Act is R2: it constrains gatekeeper self-preferencing rather than relying on disclosure alone.
• EU Carbon Border Adjustment Mechanism is R1: it assigns border liability for embedded carbon to reduce carbon-leakage incentives.

Field 17 makes system welfare inspectable before the decision

Decision Accounting is the paper’s practical R3 device. It moves the welfare record upstream so later actors can reconstruct authority, evidence, predictions, alternatives, and system burden.

• DA record: rt = actor, evidence, alternatives, prediction, reversal trigger, Field 17 welfare assessment.
• Field 17 must be decision-specific, not a vague stakeholder paragraph.
• DA can support later R1 or R2 action by creating a record of repeated welfare burden or predictable strategy harm.

Three coordinated agents can actuate R1 or R2, and four can actuate R3

The Conflictoring Lane models how a rule change becomes self-sustaining without a central coordinator. It specifies six agent types and a threshold k*.

• Agent types: legislator, regulator, court, standard-setter, plaintiff, and coalition.
• Threshold: k* = 3 for R1 and R2; k* = 4 for R3 because information architecture often needs a standard-setter or market infrastructure.
• DA without Conflictoring can become documentation of harm; Conflictoring without DA can become rule-change advocacy without a reconstructable welfare record.

The stylized Monte Carlo puts the welfare wedge far above one

The paper’s calibration is stylized, but it gives the teaching deck a concrete scale for the gap between private revenue and system-welfare burden.

• MC-verified seed 42 results use 100,000 draws and 5 channels.
• β_W median = 3.20, with 90% CI [2.46, 3.94].
• Annual revenue Π = 117.9B; W = 374.7B; ΠSA = -$256.7B; P(β_W < 1) = 0.0000%.

Valid game-change analysis must name the game and the changed component

The paper’s policy move is narrow: when MST conditions hold, reform should search for a satisficing rule transformation rather than a better move inside the inherited game.

• Gate 1: name the inherited players, strategies, payoffs, and information structure.
• Gate 2: show the Hollow Win or other welfare-destroying equilibrium.
• Gate 3: explain why taxes, subsidies, disclosure, or sanctions inside G cannot recover W.
• Gate 4: specify whether the transformation is R1, R2, or R3.