Learning objectives
After this chapter you should be able to:
- State the rule that information reaching an agent during a task is communication however it arrives, and classify a path as a convention or a message.
- Show that no fixed strategy wins the CHSH game on every round, and that shared randomness cannot lift the win rate above 75%.
- Compare a software decision with the game by truth table, and say what the mapping preserves and discards.
- Design and run a leak test with a positive control, and report a win rate with its interval and power.
- Treat a score above the bound as a trigger to audit the rig, and separate what is proved, measured and conjectured.
Opening case
A composite case, not a real engagement.
Marcus and Aiko maintain Dispatch (Chapter 14), an internal dashboard for a regional logistics company. Two coding agents work in parallel on separate tickets, one on the customer-notification service and one on the dispatcher board. Both services read a shared JobStates interface that neither agent owns. The convention file says: leave JobStates alone and adapt locally; if your ticket cannot be finished without changing it, change it.
The chapter continues from here.
What the chapter covers
- 17.1 The practical lesson: what arrives during the task is communication
- 17.2 The game and the classical bound
- 17.2.1 Converge-or-split decisions
- 17.2.2 No fixed strategy wins every round
- 17.2.3 Shared randomness does not help, and a convention is the best
- 17.2.4 What the bound assumes
- 17.3 Is the shared-interface decision this game?
- 17.3.1 The truth table
- 17.3.2 The counterexample and the stricter game
- 17.3.3 What the mapping preserves and discards
- 17.3.4 A conjecture about software
- 17.4 What the bound means for agent teams
- 17.4.1 Shared context buys a convention
- 17.4.2 Score the team, and remember the model
- 17.5 The leak test
- 17.5.1 Why a bound becomes a test
- 17.5.2 The procedure
- 17.5.3 How many rounds
- 17.5.4 Two controls before you trust a result
- 17.5.5 Hunting for the channel
- 17.5.6 Reading a result
- 17.6 The pilot as an instrument demonstration
- 17.6.1 Setup and results
- 17.6.2 The reflex result and an unresolved confound
- 17.6.3 A small factorial replication
- 17.7 Scope and limits
- 17.8 What would change these conclusions
Lab and prediction
Lab: The leak test
Feeds milestone M3. How the labs fit the project
The lab tests this prediction from the working paper the book grows from (Smith 2026a):
- P6 Configurations without explicit messages stay at or below 75%; any that exceed it reveal an identifiable channel, found after an audit of the rig
A result that contradicts a prediction, honestly reported, is a result. You are graded on accurate records and reasoned interpretation, not on agreeing with the book.
Summary
- Information that arrives during the task and depends on the other agent is communication, whether it comes through a file, a memory store or a context packet. Context fixed in advance buys a convention.
- On a converge-or-split decision (the CHSH game), 75% is a ceiling however much is shared.
- The shared-interface decision is not CHSH. It is a stricter game (neither needs a change, both change: parity accepts, the specification rejects) whose classical maximum is also 75%, so the bound holds as a necessary condition. How often software has this structure is untested.
- The leak test deals fresh fair bits through the real pipeline, with a competence check and a positive control. A score above 0.75 triggers an audit of dealing, scoring, isolation and logging; naming a channel needs further evidence. A nonsignificant result does not rule out leaks: report interval and power.
- In 200-round pilots a clean setup scored 74.5%, a planted leak 84.5% and a reflex-answering pair 26.5%. These demonstrate the instrument, not production stacks; the fix changed reasoning and lane labels together.
Key terms
- Converge-or-split decision
- a two-agent decision with private bits where success means matching actions unless both bits are unusual.
- Classical bound
- the 75% ceiling for players who share only what is fixed in advance and do not communicate.
- Convention
- a default, fixed before the round, that separated parties adopt because each expects the other to.Also used in 1, 2, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18
- Stricter game
- a game whose accepted action pairs are a subset of another's.Also used in 8
- Leak test
- dealing fresh fair bits to agents in a real pipeline and comparing the team's win rate with 0.75.Also used in 1, 2, 8, 16
- Uncounted channel
- a path carrying information about one agent's task to the other during a round, not listed in the design as communication.
- Positive control
- a planted leak that confirms the test can detect a known channel.Also used in 1, 2, 8
- Effective leak fraction (q)
- the share of rounds in which a leak was present and used correctly; win rate ≈ 0.75 + 0.25 × q.
Connections
Where this chapter and another point to each other most often.
- Chapter 1: The Coordination Problem, 1968 to Now
From Chapter 1: The pilots show that the instrument can detect a leak, not how often production stacks leak; the 1,000-round runs are in preparation (Chapters 8 and 17). - Chapter 2: The Assumption Audit: A Method That Outlasts the Tools
Place the report on the evidence ladder in Section 2.6, and say what channel the lead agent's task descriptions are. ## Further reading - Smith (2026b). The published article behind this chapter, with diagnostic questions for an architecture review. - **Cleve et al. - Chapter 8: Coordination at Scale: Shared Context vs. Shared Messages
By the two questions, a handoff packet is a message with a structured body, and its context summary behaves like compressed shared context that should be checked as a claim (Chapter 8). - Chapter 10: Design for Change, and for Agents
The design lesson belongs to Chapter 10: a written convention is necessary but not sufficient, because whether agents follow it depends on how the task asks them to decide. - Chapter 14: Configuration Management When Agents Commit
Treat a score above the bound as a trigger to audit the rig, and separate what is proved, measured and conjectured. ## Opening case A composite case, not a real team. Marcus and Aiko maintain Dispatch (Chapter 14), an internal dashboard for a regional logistics company. - Chapter 16: Roles and the Four Conditions for Assurance
But it should be counted, secured, priced and owned: logged where Chapter 16's condition 3 says channels belong, protected like any interface, costed in tokens and latency, and assigned to a named person (condition 4). - Chapter 18: Running the Whole Life Cycle: The Engineer as Manager of an Agent Team
From Chapter 18: In his run of the leak-test lab from Chapter 17 (a student's lab run, not pilot data) the pair wins 332 of 400 rounds, 83%, well above the 75% bound.
Further reading
- Smith (2026b). The published article behind this chapter, with diagnostic questions for an architecture review.
- Cleve et al. (2004), §3.1. The CHSH game as a cooperative game, with its classical value.
- Parnas (1972). The case for hiding design decisions behind module boundaries. Ask which connections a leak test would find.
- Yan (2025) and Anthropic (2025). The two practitioner positions on multi-agent design. For each, say what information it assumes crosses between agents, and who pays for it.