Designing Deals That Break the Market

The paper models the Hollow Win: A and B gain while system welfare falls

The Missing System Theorem applies when a bilateral game excludes system welfare from the payoff space. Purdue's 2010 OxyContin sales show the pattern: 3.1 billion in private revenue inside an opioid-class market linked to about 1.5 trillion per year in system welfare loss.

• Outcome code: (C=0, A=1, B=1), where the system loses and both contracting parties gain
• β_W means system welfare destroyed per dollar of industry revenue
• At the opioid-class level, peak annual revenue of about $10 billion implies β_W = 150

The SAPM corpus finds welfare loss ratios above break-even in most domains

The paper uses β_W as a revenue-denominated measure of system drawdown. Across the SAPM corpus, the estimated range is 0.76 to 51 with a mean of 8.3.

• 61 domains are analyzed in the paper's introduction
• β_W > 5 appears in 37 of 61 domains, or 60.7%
• The paper treats β_W > 5 as evidence that institutional constraints are doing more work than information gaps

A Hollow Win exists when six axioms remove system welfare from the game

The existence theorem depends on six boundary conditions: bilateral payoff closure, voluntary exchange, welfare separability, revenue-proportional drawdown, no exogenous welfare internalization, and strategic complementarity in system mining.

• Axiom 1 excludes any u_C or W term from u_A and u_B
• Axiom 4 requires expected system drawdown of at least 1 per 1 of industry revenue
• Axiom 6 says joint gains for A and B leave system welfare unchanged or worse

Disclosure cannot distinguish a Hollow Win from a win-win-win inside G

Corollary 1.1 says (0,1,1) and (1,1,1) look identical to any mechanism that only sees A and B payoffs. Both parties gain, while the missing welfare term decides whether the system was harmed.

• The bilateral payoff space contains only u_A and u_B
• Transparency within G can reveal facts without changing the payoff function
• The falsification test asks for a self-correcting Hollow Win with β_W > 5 and no game-form change

Mechanisms confined to A and B payoffs cannot implement C=1

The mechanism design impossibility follows because incentive compatibility is written over A and B allocations, while welfare preservation requires conditioning on W. Under Axiom 1, W is absent from the mechanism's objective.

• A direct revelation mechanism can preserve welfare only if it can condition on W
• Axiom 5 rules out costless internalization inside G
• The fix must transform the game form rather than optimize inside the bilateral game

Positive-revenue Hollow Wins have β_W at least 1 in expectation

The lower-bound theorem defines β_W = -dW/dΠ. If revenue Π is positive and the six axioms hold, Theorem 1 gives dW < 0 and Axiom 4 gives β_W ≥ 1 in expectation.

• Π is industry annual revenue, not profit or market capitalization
• The metric uses the paper's iron-law revenue denominator
• β_W below 1 would falsify the theorem only in a domain where the six axioms hold

Abacus turned a $15 million fee into β_W = 7,933

Goldman Sachs structured Abacus 2007-AC1, a synthetic CDO referencing subprime RMBS. Paulson & Co., which was short the same assets, helped select the portfolio; IKB and ACA were told an independent collateral manager selected it.

• Goldman received 15 million in structuring and placement fees and about 1 billion in short profits
• Synthetic CDOs outstanding in 2007 totaled about $2.2 trillion
• The paper attributes 1% of the IMF's 11.9 trillion crisis cost to synthetic CDO market structure: 119 billion

Purdue's OxyContin campaign produces β_W = 71.4 on $35 billion in revenue

Purdue marketed OxyContin from 1996 to 2017 while downplaying addiction risk. The sales force grew from 318 in 1996 to 671 in 2000, and OxyContin reached a peak 80% share of long-acting opioid prescriptions.

• Purdue generated about $35 billion in OxyContin revenue
• The paper estimates $2.5 trillion in cumulative opioid system welfare loss from 2000 to 2020
• The Sackler family extracted about 10 billion to 13 billion in dividends

Facebook's engagement feed produces β_W = 1.54 against 2021 ad revenue

The Facebook case treats News Feed ranking as an engagement-maximizing exchange between Meta and advertisers. Users supply attention and data, while system costs appear in mental health, democratic institutions, and Myanmar-related humanitarian harm.

• Meta generated $117 billion in advertising revenue in 2021
• The paper's conservative system cost estimate totals $180 billion
• An internal 2019 slide stated: "We make body image issues worse for 1 in 3 teen girls"

The F-35 program produces β_W = 1.25 through excess cost and dependency

The defense procurement case centers on the DoD, Lockheed Martin, and the Joint Program Office. The bilateral relationship is stable because Lockheed receives guaranteed revenue and the DoD receives a platform no other contractor can provide.

• Lockheed's cumulative F-35 contract value exceeds $400 billion from 2001 to 2023
• The lifecycle cost estimate is 1.7 trillion through 2070, compared with a 2001 development and production estimate of 233 billion
• The paper estimates $500 billion in excess cost and reports a 2023 mission-capable rate of about 60%

Field 17 is the paper's rule change for material decisions

The required transformation is mandatory inclusion of system welfare impact in every material decision record through the 17-field Decision Accounting protocol. Field 17 moves W into the decision architecture instead of leaving it outside the game.

• Field 17 records system welfare impact and makes it part of execution review
• Abacus Field 17 would have captured systemic use without productive asset creation
• Purdue Field 17 would have captured addiction, family breakdown, and workforce exit before those costs hit the public

The target is game-form change, not better bilateral optimization

The paper's policy implication is that markets break when private deals mine omitted system welfare. Disclosure and voluntary reporting do not alter the equilibrium unless system welfare becomes a binding term in the decision process.

• The General Game-Change Conjecture names a transformation R for each domain
• The paper estimates a Reform Dividend across SAPM domains from recapturing system welfare losses
• The closing design task is to make deals that do not break the market