Repeated game strategist

Repeated Game Strategist

One-shot logic destroys value in repeated interactions. This skill chooses the strategy that survives the long run.

What this skill is

A workflow for analyzing repeated interactions (competitors, partners, suppliers, customers, internal teams) where the same parties meet again and again. Applies the folk theorem, computes the critical discount factor for cooperation to be sustainable, evaluates classic strategies - Tit-for-Tat (TFT), grim trigger, generous TFT, and win-stay-lose-shift (Pavlov) - and recommends a policy with explicit triggers for retaliation, forgiveness, and reset.

What it solves

• Treating repeated competitive moves with prisoner's-dilemma defection logic
• Retaliating reflexively to noise (treating an accident as deliberate defection)
• Never retaliating to genuine defection (training the other side to keep defecting)
• Cooperation strategies that unravel in finite horizons without commitment
• Ignoring reputation effects when private information enters the game

When to invoke

• Setting a multi-year competitive posture (cooperate or compete on which dimensions)
• Structuring an ongoing supplier or partner relationship
• Designing a retaliation policy when a competitor breaks an implicit norm
• Procurement strategy with repeat suppliers
• Internal team dynamics (cross-functional cooperation patterns)
• Customer retention strategies with renegotiation cycles

Phase 1: Specify the repeated interaction

• Players - typically 2; multi-player is harder to coordinate
• Stage game - payoff matrix for one round
• Time horizon - finite (and known? unknown?) or infinite
• Frequency - how often does the game repeat?
• Discount factor δ - how much do future payoffs count? δ ≈ 1 / (1 + discount rate per period)
• Observability - can each player perfectly observe the other's action? With what lag?
• Noise - can actions or outcomes be misinterpreted?

If the stage game is not a true social dilemma (cooperation Pareto-dominates one-shot Nash equilibrium), repeated-game analysis adds little.

Phase 2: Identify the cooperation gain

Compute payoffs in each state:

• (C, C) - both cooperate
• (D, D) - both defect (one-shot Nash equilibrium)
• (C, D) - you cooperate, they defect (sucker payoff)
• (D, C) - you defect, they cooperate (temptation payoff)

Standard Prisoner's Dilemma (PD) ranking: T > R > P > S, where R = mutual cooperation, T = temptation, P = mutual punishment, S = sucker.

The cooperation gain = R − P, sustained over many periods.

Phase 3: Critical discount factor

For cooperation under grim trigger:

δ ≥ (T − R) / (T − P)

If your δ exceeds this threshold, cooperation is sustainable. If not, you need a different mechanism or to accept the one-shot equilibrium.

Levers to raise δ:

• Longer time horizon (extend the relationship)
• Higher frequency of interaction
• Lower volatility (more stable future)
• Higher value of the relationship to each party

Levers to lower δ (when you want to break a collusive equilibrium against you):

• Bring in a third player who plays one-shot
• Shorten the time horizon (signal exit)
• Reduce observability (harder to detect defection)

Phase 4: Choose a strategy

Strategy	Mechanism	Strength	Weakness
Always cooperate	Unconditional C	Maximizes mutual gain if other reciprocates	Exploited by any defector
Always defect	Unconditional D	Robust to exploitation	Forfeits cooperation gain
Tit-for-Tat (TFT)	Cooperate first, then copy opponent	Nice, retaliatory, forgiving, clear	Locks into mutual defection on a single error
Generous TFT	TFT but occasionally forgives a defection	Recovers from noise	Slightly exploitable
Grim trigger	Cooperate until first defection, then defect forever	Maximum deterrence	Catastrophic on a single error or noise
Win-stay, lose-shift (Pavlov)	Repeat last action if it paid; switch otherwise	Strong in noisy environments	Cooperates with unconditional defectors
Tit-for-two-tats	Defect only after two consecutive defections	Robust to noise	Slow to deter sustained defection

Decision guide:

• High observability plus low noise → TFT or grim trigger
• Noisy observation → generous TFT, tit-for-two-tats, or Pavlov
• Finite known horizon → reputation effects required to avoid unraveling

Phase 5: Reputation effects (incomplete information)

In a finite-horizon game, cooperation unravels via backward induction - unless players have private information about their type.

The Kreps-Milgrom-Roberts-Wilson reputation effect: if there's a small probability you're a "crazy" TFT type, even a rational opponent will cooperate for most of the finite horizon.

Implication: invest in reputation - observable history of cooperation, slow forgiveness, transparent retaliation - to make the "crazy type" prior credible.

Phase 6: Retaliation policy

Define when to retaliate, how hard, for how long, and when to reset:

Element	Question	Recommendation
Trigger	What action constitutes defection?	Specific, observable, public
Detection threshold	How sure must we be?	Higher with noise
Severity	How proportionate?	Tit-for-tat scale
Duration	How long?	Just long enough to restore deterrence
Forgiveness	When do we return to cooperation?	After observable peace gesture
Public posture	Do we announce retaliation?	Yes - improves deterrence
Asymmetric cost	What's the cost to you of retaliating?	Don't escalate beyond your sustainable cost

Phase 7: Multi-player extensions

When more than two players interact:

• Cooperation harder to sustain (more chances for someone to defect)
• Need monitoring across many players
• Standards, norms, and industry conventions emerge as coordination devices
• Public statements can serve as commitment to multilateral enforcement
• Watch for legal and regulatory limits on tacit coordination among competitors

Output

• Game specification: stage payoffs, horizon, frequency, δ, observability, noise
• Critical discount factor and whether cooperation is sustainable
• Recommended strategy from the strategy table with reasoning
• Retaliation policy: trigger, severity, duration, forgiveness, public posture
• Reputation investment plan
• Trigger conditions to revisit the strategy (e.g., observed pattern change)
• Watch-list: behaviors that would force a switch in strategy

Operating rules

Always

• Compute the critical discount factor before recommending cooperation
• Match the strategy to the noise level
• Define a public, proportional retaliation policy
• Invest in reputation when horizon is finite
• Distinguish a single accident from a defection pattern

Never

• Apply one-shot logic to a clearly repeated game
• Choose grim trigger in a noisy environment
• Retaliate on insufficient observation
• Defect at the announced last round (it unravels backward)
• Confuse tacit coordination with legal collusion among competitors