Use this skill when you face a situation where:
Preconditions: you have at least one of:
Agent: Before starting, confirm: (1) how many players are involved, (2) whether this is a one-shot or repeated interaction, and (3) whether the user wants only a diagnosis or a full cooperation mechanism design. The mechanism design is the core deliverable.
User prompt → Identify: who are the players, what can each choose, what are the rough payoffs?
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Environment → Are there documents describing the situation, history, or prior agreements?
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Gap analysis → Do I have enough to build a payoff table and assess the discount rate?
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Missing critical info? ──YES──→ ASK (one question at a time)
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NO
↓
PROCEED with diagnosis and mechanism design
→ Check prompt for: named parties, "we vs. they" language, player count
→ If missing, ask: "Who are the parties in this situation? Are they a small identifiable group or a large anonymous one?"
→ Check prompt for: specific behaviors like pricing, output levels, investment, restraint
→ If missing, ask: "What does cooperation look like in practice — what would each party have to do or give up? And what does defection look like — what is the tempting unilateral advantage?"
→ Check prompt for: "no matter what they do," "everyone is better off if all cooperate but each has an incentive to cheat," outcomes from prior interactions
→ If missing, ask: "When you consider your best move — is it to defect regardless of what the other party does? Or does your best move depend on what they do?"
→ Check prompt for: contract duration, relationship history, expected future interactions
→ If missing, ask: "Is this a one-time interaction or an ongoing relationship? If ongoing, is there a foreseeable end date?"
→ Relevant for: assessing whether trust has already been destroyed, choosing repair strategies
→ Relevant for: mechanism design — hidden defection requires different solutions than visible defection
→ Relevant for: Ostrom principle 1 (clear membership) and end-game defection risk
Ask ONE question at a time, most critical first. Show what you already know before asking. State why you need the information.
Use TodoWrite to track steps before beginning.
TodoWrite([
{ id: "1", content: "Diagnose: confirm prisoners' dilemma vs coordination problem", status: "pending" },
{ id: "2", content: "Map payoffs: build rough payoff table with cooperation surplus", status: "pending" },
{ id: "3", content: "Assess discount rate: calculate cooperation sustainability threshold", status: "pending" },
{ id: "4", content: "Score mechanism prerequisites: detection, clarity, certainty, size, repetition", status: "pending" },
{ id: "5", content: "Select and design cooperation mechanism from resolution menu", status: "pending" },
{ id: "6", content: "For commons/multiperson: apply Ostrom's design principles checklist", status: "pending" },
{ id: "7", content: "Produce cooperation design plan with implementation steps", status: "pending" }
])
ACTION: Determine whether the situation is a genuine prisoners' dilemma, a coordination problem, or something else. This diagnosis determines the entire remedy.
WHY: The treatments are fundamentally different. A prisoners' dilemma has a dominant strategy to defect — each player is better off defecting regardless of what others do. A coordination problem has multiple equilibria — once aligned on the same convention (QWERTY, driving on the right, common standards), no one wants to deviate unilaterally. Applying cooperation mechanisms to a coordination problem is wasted effort; what's needed is a focal point or a critical mass to tip behavior.
Two-question diagnostic:
If YES to both → prisoners' dilemma. Defection is dominant. Proceed through this skill.
If NO to question 1 (defection hurts me when others cooperate) → coordination problem. The issue is aligning expectations, not suppressing defection. See coordination notes in References.
If YES to question 1 but NO to question 2 → asymmetric game. One party may have a dominant defection strategy while the other's best response depends on context. Requires separate analysis.
Also check: is this zero-sum? In a zero-sum game, every gain by one player comes at exactly equal cost to another. Zero-sum games have no cooperation surplus — there is nothing to gain from mutual restraint. The prisoners' dilemma is NOT zero-sum: both players are better off in the mutual cooperation cell than in the mutual defection cell.
Confirm the cooperation surplus exists: There must be a combination of choices where all parties are better off than in the mutual-defection equilibrium. If no such combination exists, this is not a prisoners' dilemma.
Mark Step 1 complete in TodoWrite.
ACTION: Construct a rough payoff table showing the four cells: (Cooperate, Cooperate), (Cooperate, Defect), (Defect, Cooperate), (Defect, Defect). For multiperson dilemmas, show how collective payoff changes as the number of cooperators rises.
WHY: The payoff table makes the temptation and its cost concrete. Without it, the mechanism design is abstract. The payoff structure also determines which mechanisms are viable — specifically, the ratio of the one-period defection gain to the ongoing cooperation gain determines the discount-rate threshold (Step 3).
Standard prisoners' dilemma payoff ordering (for each player):
Quantify if possible:
For multiperson / commons situations: Replace the 2x2 table with a contribution schedule showing how each party's payoff changes as the number of cooperators increases. Key feature: each defector gains a fixed amount regardless of how many others defect, but spreads a cost across all cooperators. This is the "contribution game" structure.
Mark Step 2 complete in TodoWrite.
ACTION: Determine the maximum interest rate (discount rate) at which sustained cooperation is rational. If the actual interest rate or impatience level is below this threshold, cooperation through repeated play is sustainable without external enforcement.
WHY: The key insight of repeated-game analysis is that defection gains a short-term advantage but destroys long-term cooperation value. Whether defection is worth it depends on how much you value the future. If you are very impatient (high discount rate), the future is worth little and defection becomes attractive even knowing the relationship will collapse. If you value the future sufficiently (low discount rate), the prospect of losing ongoing cooperation outweighs the temptation to cheat today.
Formula:
Cooperation is self-sustaining if the interest rate r satisfies:
r < (R − P) / (T − R)
Where:
Worked example (from Ch. 3, Rainbow's End / B.B. Lean pricing):
What raises the sustainability threshold (makes cooperation easier):
What lowers the sustainability threshold (makes cooperation harder):
End-game problem: In a finite repeated game with a known final period, backward induction unravels cooperation all the way to round 1. Solution: eliminate the clear end-game — use indefinite time horizons, rolling contracts, or overlapping agreements so there is no obvious "last round."
Mark Step 3 complete in TodoWrite.
ACTION: Evaluate the situation against five prerequisites for an effective punishment-based cooperation mechanism. Each gap identifies a specific design problem to solve.
WHY: Punishment is the most common mechanism for sustaining cooperation. But punishment only deters defection if it meets specific structural requirements. A gap in any one of the five areas undermines the entire mechanism. Identifying which prerequisite is weak tells you exactly what the mechanism design needs to fix.
The five prerequisites:
1. Detection — Can defection be observed, attributed to the right party, and detected quickly?
2. Clarity — Are the rules of cooperation and the boundaries of acceptable behavior unambiguous?
3. Certainty — Is punishment guaranteed when defection occurs? Is cooperation reliably rewarded?
4. Size — Is the punishment large enough to deter, but not so large that errors cause catastrophic spirals?
5. Repetition — Is there a sufficient "shadow of the future"? (Covered in Step 3 — confirm result applies here.)
Mark Step 4 complete in TodoWrite.
ACTION: Choose the appropriate mechanism from the resolution menu below. Mechanisms are ordered from lowest to highest external requirement. Select the lowest-level mechanism that is feasible given the prerequisites scored in Step 4.
WHY: Not every situation requires the same intervention. Using heavy external enforcement when self-enforcement would work wastes resources and creates regulatory risk (antitrust exposure for firms). Using self-enforcement when the prerequisites are missing produces predictable failure. Matching mechanism to situation is the core design task.
Resolution Menu (escalating external requirement):
Level 1 — Self-enforcing repeated play (tit-for-tat or generous variant)
Use when: discount rate is below threshold (Step 3 result), players interact repeatedly, detection is feasible.
How it works: Players cooperate initially, then mirror the other's last move. The credible threat of future retaliation deters current defection.
Standard tit-for-tat: Cooperate first; replicate opponent's last move every subsequent period.
Generous tit-for-tat (preferred in practice): Cooperate first; punish sustained defection but forgive isolated defections. The tamarin monkey threshold: tolerate up to 1 defection, punish 2 consecutive defections.
Implementation checklist:
Level 2 — Mutual promises with escrow or simultaneous commitments
Use when: Tit-for-tat is viable but trust is currently depleted; players need a credibility boost to restart cooperation.
How it works: Both parties make simultaneous promises and deposit promised payments (or penalties for non-performance) in a neutral escrow account. Neither can renege without forfeiting the escrow. Converts soft promises into hard commitments.
Use cases: Restart of cooperation after a defection episode; situations where one party is less patient and needs a structural guarantee; situations where the relationship is new and no reputation exists yet.
Level 3 — Reputation and linkage across multiple interactions
Use when: The dyadic interaction has insufficient cooperation surplus to sustain self-enforcement on its own, but the parties interact in multiple dimensions.
Reputation mechanism: Public record of each party's cooperation history creates external cost for defection beyond the bilateral relationship. A firm that cheats on a pricing arrangement faces skepticism from future trading partners, lenders, and employees. Works best when: the reputation is observable to third parties who matter, defection is clearly attributable, and the relationship horizon extends far enough to make the reputation investment worthwhile.
Linkage mechanism: Bundle multiple interactions so defecting in one dimension risks the entire relationship. Cooperation surplus across all linked interactions must exceed the temptation to defect in any one. Warning: linkage scales both gains and defection gains proportionally if all dimensions have identical payoff structures — benefit comes only from asymmetries across dimensions.
Level 4 — Third-party intervention and external enforcement
Use when: Self-enforcement is not viable (relationship is too short, discount rate too high, detection too imperfect), and parties cannot credibly commit to punishments themselves.
Options:
Level 5 — Ostrom commons governance (multiperson dilemmas)
Use when: The dilemma involves a large group managing a shared resource (fishery, groundwater, pasture, shared infrastructure, open-source contribution, common standards).
Apply all eight Ostrom design principles as a checklist. Each principle maps to a specific prerequisite gap:
Ostrom's warning: "The dilemma never fully disappears, even in the best operating systems. No amount of monitoring or sanctioning reduces the temptation to zero. Effective governance systems cope better than others — they do not eliminate the problem."
Mark Step 5 complete in TodoWrite.
ACTION: If the dilemma involves more than two players and a public good or shared resource, assess the contribution game structure: each party's dominant strategy is to free-ride; collective optimum requires all to contribute.
WHY: Multiperson prisoners' dilemmas have a specific feature that bilateral dilemmas lack: each defector's gain is fixed (they free-ride on others' contributions), but each defector imposes a cost spread across ALL cooperators. In the 4-player contribution game: contributing $1 to the pool raises total benefit by $2 (after doubling), but the contributor receives only $0.50 of the gain ($1.50 goes to others). This makes free-riding dominant regardless of what others do.
Contribution game checklist:
Mark Step 6 complete in TodoWrite.
ACTION: Write a structured cooperation design plan covering the full analysis from Steps 1-6.
WHY: The plan must be specific and actionable. "Use tit-for-tat" is not useful. "Define price cuts of more than 5% as defection, respond with a 10% price cut effective next catalog cycle, forgive single-period deviations, treat two consecutive deviations as intentional" is useful — it specifies the operational terms the parties need to implement.
HANDOFF TO HUMAN — the agent produces the plan; the human negotiates, implements, and monitors.
Plan format:
# Cooperation Design Plan
## Game Diagnosis
**Type:** [Prisoners' Dilemma / Coordination Problem / Asymmetric / Not applicable]
**Cooperation surplus exists:** [Yes/No — the mutual cooperation cell vs. mutual defection cell]
**Payoff structure:**
| | Other: Cooperate | Other: Defect |
|---|---|---|
| You: Cooperate | R = [value] | S = [value] |
| You: Defect | T = [value] | P = [value] |
**Dominant strategy:** [Defect / Cooperate / Context-dependent]
## Discount-Rate Assessment
**One-period defection gain (T − R):** [value]
**Annual cooperation value at stake (R − P):** [value]
**Break-even interest rate:** [calculation and result]
**Self-enforcement viable?** [Yes if actual rate < break-even / No if above]
## Prerequisite Gaps
| Prerequisite | Status | Gap Description |
|---|---|---|
| Detection | [Strong/Weak/Missing] | [specific gap] |
| Clarity | [Strong/Weak/Missing] | [specific gap] |
| Certainty | [Strong/Weak/Missing] | [specific gap] |
| Size (minimum deterrent) | [Strong/Weak/Missing] | [specific gap] |
| Repetition / shadow of future | [Strong/Weak/Missing] | [specific gap] |
## Recommended Mechanism
**Level selected:** [1–5 from resolution menu]
**Mechanism:** [Name and brief description]
**Rationale:** [Why this level fits the situation]
## Implementation Steps
1. [Operational definition of cooperation and defection in this context]
2. [Monitoring arrangement: how, by whom, with what frequency]
3. [Response rule: specific trigger and specific response]
4. [Forgiveness threshold: when to restore cooperation]
5. [Communication plan: how to make the strategy clear to all parties]
6. [Escalation path: if self-enforcement fails, what is the next level?]
## Risks and Anti-Patterns
- **End-game defection risk:** [Is there a visible final period? How to address?]
- **Punishment spiral risk:** [Is generous tit-for-tat needed? What forgiveness threshold?]
- **Player composition risk:** [Are new entrants expected? How does the mechanism handle them?]
- **Boom/bust defection timing:** [When is defection temptation highest? Special provisions needed?]
## For Commons/Multiperson Situations
Ostrom principle compliance:
- [ ] Defined boundaries
- [ ] Rules match local conditions
- [ ] Graduated sanctions
- [ ] Automatic detection embedded in operations
- [ ] Locally designed rules
- [ ] Conflict resolution mechanisms
- [ ] External recognition
- [ ] Nested governance (for large systems)
Mark Step 7 complete in TodoWrite.
Example 1: Pricing cartel between two mail-order retailers
Situation: Rainbow's End (RE) and B.B. Lean (BB) both price shirts at $70 when both could price at $80 and each earn $72,000 vs. $70,000 per year. Each firm cuts to $70 because it's the dominant strategy: cutting while the other holds at $80 yields $110,000; holding at $80 while the other cuts yields only $24,000.
Diagnosis: Classic 2-player prisoners' dilemma. T=$110k, R=$72k, P=$70k, S=$24k. Defection dominant for both.
Discount-rate calculation: (R−P)/(T−R) = ($72k−$70k)/($110k−$72k) = $2k/$38k = 5.26%. If prevailing interest rate < 5.26%, tacit cooperation at $80 is self-sustaining.
Mechanism: Level 1 (self-enforcing repeated play). Detection: price lists are publicly observable. Clarity: define "defect" as cutting below $80. Response: immediately match any price cut in next catalog. Forgiveness: if other party restores $80 pricing, match that too. Communication: a "most-favored-customer" clause makes the automatic response policy public, removing ambiguity. Anti-pattern avoided: no explicit agreement is reached (antitrust risk); cooperation is purely tacit.
Example 2: Fishery commons overexploitation
Situation: New England fishing fleet: each captain has incentive to catch as much as possible before others do; result is collapse of species after species (Atlantic halibut, ocean perch, haddock).
Diagnosis: Multiperson prisoners' dilemma (contribution game). Each additional catch by one captain reduces the stock for all others. Dominant strategy: fish aggressively regardless of what others do.
Discount-rate calculation: Not determinative on its own — relationship continues indefinitely but individual boats can't unilaterally enforce rules against strangers.
Mechanism: Level 5 (Ostrom commons governance). Apply 8-principle checklist:
Example 3: Coordination problem misdiagnosed as cooperation problem
Situation: Ivy League colleges keep overspending on athletics even though the relative standings stay the same. "Each school would be better off if we all limited spring training to one day."
Diagnosis check: "If other schools limit training, should I limit training?" → Yes, my performance improves no more than theirs, but I save costs. "If other schools don't limit training, should I limit training?" → No, I'd be at a disadvantage. This is NOT a prisoners' dilemma. Defection is NOT dominant regardless of others' choices. The best response to "others cooperate" is to cooperate; the best response to "others defect" is to defect. This is a coordination problem.
Mechanism: Not Level 1-5 from the resolution menu. Instead: establish a focal point for the cooperative equilibrium through a collective agreement with clear enforcement (the Ivy League agreement limiting spring training to one day). Once the convention is established and everyone expects everyone else to comply, compliance becomes self-sustaining without punishment — because no one wants to be the only school overdoing training when no one else is.
Key distinction that matters: if this were a genuine prisoners' dilemma, the agreement would keep collapsing despite everyone's stated preference for cooperation. In coordination problems, a credible agreement is usually sufficient because there is no dominant strategy to defect — just a fear that others won't cooperate.
This skill is licensed under CC-BY-SA-4.0.
Source: BookForge — The Art of Strategy: A Game Theorist's Guide to Success in Business and Life by Avinash K. Dixit, Barry J. Nalebuff.
This skill is standalone. Browse more BookForge skills: bookforge-skills
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