Game Theory Tit For Tat

The Four Qualities

Why TFT Wins:

┌──────────────┬───────────────────────────────────────────────────┐
│   NICE       │ Never defects first                               │
│              │ Starts with cooperation and good faith            │
├──────────────┼───────────────────────────────────────────────────┤
│   RETALIATORY│ Immediately punishes defection                    │
│              │ Prevents exploitation                             │
├──────────────┼───────────────────────────────────────────────────┤
│   FORGIVING  │ Returns to cooperation after one punishment       │
│              │ Enables recovery of relationships                 │
├──────────────┼───────────────────────────────────────────────────┤
│   CLEAR      │ Pattern is easy to recognize                      │
│              │ Opponents learn cooperation is rewarded           │
└──────────────┴───────────────────────────────────────────────────┘

Understanding the Payoff Matrix

Prisoner's Dilemma Payoffs:

                    Partner's Choice
                    ┌─────────────┬─────────────┐
                    │  COOPERATE  │   DEFECT    │
         ┌──────────┼─────────────┼─────────────┤
    Your │COOPERATE │  Win-Win    │  You Lose   │
   Choice│          │  (3, 3)     │  (0, 5)     │
         ├──────────┼─────────────┼─────────────┤
         │ DEFECT   │  You Win    │  Lose-Lose  │
         │          │  (5, 0)     │  (1, 1)     │
         └──────────┴─────────────┴─────────────┘

In single games: Defection seems better (5 > 3)
In repeated games: Mutual cooperation wins (3+3+3... > 5+1+1...)

Application Framework

Step 1: Assess the Interaction Type

Is TFT appropriate?

Repeated interaction?
├── YES → TFT applies
└── NO  → One-shot game (different strategy needed)

Shadow of the future?
├── Will interact again → TFT works well
└── No future interaction → Less effective

Can they observe your response?
├── YES → TFT signals clearly
└── NO  → Communication needed

Step 2: Determine Your Starting Position

First Move Decision:

New relationship?
└── COOPERATE (be nice)

Existing relationship?
├── Their last action was cooperative → COOPERATE
└── Their last action was defection → DEFECT (once)

After punishment?
└── If they cooperate again → COOPERATE (forgive)

Step 3: Execute and Communicate

Output Template

After analyzing a situation, document as:

## Tit for Tat Analysis

**Situation:** [Description]

**Date:** [Date]

### Relationship Assessment

| Factor                | Status                                       |
| --------------------- | -------------------------------------------- |
| Repeated interaction? | Yes/No                                       |
| History               | [Cooperative/Mixed/Adversarial]              |
| Their last move       | [Cooperate/Defect]                           |
| Current state         | [In good standing/Punishment phase/Recovery] |

### Recommended Action

**Action:** [Cooperate/Defect]

**Rationale:** [Based on which TFT principle]

### Communication Plan

**If Cooperating:**

- [What to say/do]
- [How to reinforce positive dynamic]

**If Defecting (Retaliating):**

- [Specific response to their defection]
- [Clear signal that cooperation will resume if they cooperate]
- [Avoid over-punishment]

### Exit Conditions

| If They...            | Then I...                    |
| --------------------- | ---------------------------- |
| Return to cooperation | Immediately forgive          |
| Continue defecting    | Continue matching            |
| Escalate              | [Boundary for disengagement] |

Real-World Applications

Workplace Relationships

Scenario: Coworker missed deadline affecting your work

TFT Response:

Be Nice (initially):
├── Assume competence and good faith
├── Give benefit of doubt first time
└── Don't preemptively retaliate

Be Retaliatory (this incident):
├── Address directly: "The report wasn't sent as agreed"
├── Ask what happened
├── Set clear expectation for next time
└── Don't let it slide (prevents exploitation)

Be Forgiving (after):
├── Once addressed and they commit to improve
├── Drop the issue completely
├── Don't bring it up in future interactions
└── Don't hold a grudge

Be Clear:
├── Your response should be predictable
├── They should know: cooperate = good, defect = consequences
└── Make pattern obvious so they can adjust

Business Negotiations

Scenario: Partnership negotiation

TFT Approach:

Opening (Nice):
├── Make first good-faith offer or concession
├── Signal you want win-win outcome
└── Don't start with extreme position

Response to Their Move:

If they make reasonable offer:
└── Match with reasonable counter

If they lowball aggressively:
├── Match their firmness
├── Don't concede further
└── Show you won't be exploited

Recovery Path:
├── Moment they move to reasonable position
├── You move to reasonable position too
└── Signal: cooperation = path to deal

Personal Relationships

Scenario: Friend cancelled plans last minute

TFT Application:

Nice (default):
├── Assume good reason
├── Don't catastrophize
└── Be understanding this time

Retaliatory (if pattern emerges):
├── Set boundary: "When plans change last minute, it affects me"
├── Communicate clearly
├── Reduce investment in future plans with them

Forgiving (if they adjust):
├── When they make effort to be reliable
├── Immediately return to full engagement
├── Don't "echo" past cancellations

Handle Noise:
├── Clarify intent before retaliating
├── "When you cancelled, was something wrong?"
├── Miscommunication shouldn't start death spiral

Known Weaknesses

1. Noise Problem

The Death Spiral:

Misunderstanding occurs:
├── You cooperated, they perceived defection
├── They defect in response
├── You defect in response
├── Alternating defections continue
└── Both lose, neither recovers

Solution: Generous Tit for Tat
├── Occasionally forgive defection (10% random)
├── Breaks accidental cycles
├── Better in "noisy" environments
└── Communicate to clarify perceived defections

2. Credibility Problem

The Punishment Paradox:

After they defect:
├── TFT says: retaliate
├── But: retaliation is costly to you too
├── Rational choice: forgive and return to cooperation
└── If they know this, threat isn't credible

Solution: Commit to retaliation
├── Make punishment automatic
├── Reputation for following through
├── Short-term cost for long-term credibility

Variants

Integration with Other Methods

Quick Reference

TIT FOR TAT DECISION TREE

New interaction?
└── COOPERATE (be nice)

They just cooperated?
└── COOPERATE (reward)

They just defected?
├── DEFECT once (retaliate)
└── Then if they cooperate → COOPERATE (forgive)

Unclear if defection was intentional?
├── COMMUNICATE first
└── "Was that intentional?" before retaliating

Stuck in defection cycle?
├── Unilaterally cooperate once
├── See if they break cycle
└── If not, reassess relationship

Questions for Situational Analysis

When applying TFT, consider:

1. What's your primary goal?

   • Repair relationship (break death spiral)
   • Build new partnership
   • Navigate competitive environment

2. How noisy is your environment?

   • High noise → Use Generous TFT
   • Low noise → Standard TFT works

3. Individual or group?

   • 1:1 → TFT works well
   • Group → More complex dynamics

Resources

• The Evolution of Cooperation - Robert Axelrod
• Veritasium: The Prisoner's Dilemma
• Game Theory 101
• Behavioral Game Theory - Colin Camerer