← Docs ← Home
Crt Theory

Cryptographic Reciprocity Theory (CRT)

Cryptographic Reciprocity Theory (CRT) is a framework for constructing systems in which cooperation emerges from rational self-interest over extended time horizons.

This document describes the theory without philosophical interpretation.


Core Premises

CRT does not assume altruism or moral alignment.
It assumes that agents respond to: - Incentives (what benefits them) - Observability (what others can see) - Delayed consequences (what happens later)

The theory is based on three premises:

1. Behavior is shaped by repeated interaction

Single encounters favor defection (betrayal).
Repeated encounters favor cooperation (tit-for-tat).

When agents know they will interact again, cooperation becomes more valuable than immediate gain.

2. Trust is an emergent property, not a prerequisite

You don't need to trust someone before cooperating with them.
Trust emerges from repeated, predictable behavior over time.

CRT systems make behavior observable so trust can develop naturally.

3. Long-term commitments require mechanisms that outlast individuals

Promises fade.
Contracts can be breached.
Institutions can be captured.

Cryptographic commitments persist regardless of: - Who created them - What authority enforces them - Whether the creator is still alive


Theoretical Foundation: Game Theory

CRT builds on the Iterated Prisoner's Dilemma.

In a single-round Prisoner's Dilemma: - Defection (betrayal) is always optimal - Cooperation is irrational

In repeated games: - Defection in round N hurts you in round N+1 - Cooperation becomes rational over time - Tit-for-tat strategies emerge as optimal

CRT extends this by: - Making behavior observable (blockchain records) - Making history persistent (immutable ledger) - Extending time horizons (21-year cycles)


Cryptographic Primitives Used

CRT uses these Bitcoin primitives:

1. Public Key Cryptography

  • Identities are public keys
  • Authentication is signature verification
  • No passwords or accounts required

2. Time-Locked Transactions

  • Commitments encoded as Bitcoin transactions
  • Unlocking requires specific block height or timestamp
  • Cannot be reversed once created

3. Partially Signed Bitcoin Transactions (PSBTs)

  • Proof of funds without spending
  • Multi-party coordination
  • Verifiable commitments

4. Output Descriptors

  • Complex spending conditions
  • Multi-signature schemes
  • Covenant-like structures

How CRT Systems Work

Step 1: Identity Creation

Participant generates a Bitcoin key pair.
Public key becomes their identity.
Private key remains secret.

No registration required.
No email or phone number.
Just cryptography.

Step 2: Commitment Creation

Participant creates a time-locked transaction: - Locks funds until block height X - Signs transaction with private key - Broadcasts to Bitcoin network

The commitment is now: - Publicly verifiable - Immutable - Enforceable by consensus rules

Step 3: Behavior Observation

Other participants can: - See the commitment on blockchain - Verify the signature - Track the participant's history - Update their assessment of reliability

This is reputation without a centralized database.

Step 4: Consequence Propagation

If participant defects: - Their history shows the defection - Future partners see this - Cost of cooperation with them increases

If participant cooperates: - Their history shows reliability - Future partners prefer them - Access to valuable relationships improves


Why Time-Locks Matter

Time-locks solve the commitment problem.

Without time-locks: - Promises can be broken - Commitments are cheap - Signals are unreliable

With time-locks: - Breaking commitment means losing funds - Making commitment is costly - Signals are expensive to fake

This creates credible commitment.


Reputation Model

CRT reputation is not a score.
It is an observable history.

Traditional reputation systems: - Collapse identity to a number (5 stars, 1000 points) - Hide context and nuance - Can be gamed or manipulated

CRT reputation: - Preserves full history of actions - Maintains context (when, with whom, under what conditions) - Cannot be erased or edited

Participants form their own judgments based on observable facts.


Incentive Alignment

CRT aligns incentives through:

1. Delayed Consequences

Short-term defection creates long-term costs.
Reputation damage compounds over time.

2. Observable History

Actions cannot be hidden or denied.
Blockchain provides permanent record.

3. Symmetric Rules

No one has privileged access.
Everyone faces the same incentives.

4. Costly Signaling

Time-locked commitments are expensive to fake.
Only serious participants will make them.


Mathematical Model (Simplified)

Let: - A = set of agents with persistent identities - L = public ledger of all actions - T = time horizon (e.g., 21 years)

For each agent i at time t: - Hi,t = history of actions up to time t - Ri,t = reputation derived from Hi,t

Agent i chooses strategy si to maximize:

V_i = Σ (payoff_t × discount_factor^t)

Where: - payofft depends on actions and reputation - discount_factor < 1 (future matters less than present)

In CRT systems: - Defection at time t reduces Ri,t+1 - Lower reputation reduces future payoffs - Long time horizon T makes future losses significant

Thus, cooperation becomes rational.


Comparison to Traditional Systems

Traditional CRT
Trust required upfront Trust emerges from observation
Reputation controlled by platform Reputation derived from blockchain
Commitments enforced by law Commitments enforced by cryptography
Exit may be restricted Exit always possible
Rules can be changed arbitrarily Rules are transparent and symmetric

Limitations

CRT cannot: - Force cooperation (agents can always defect) - Eliminate all uncertainty (unknown unknowns remain) - Work with fully anonymous participants (identity must be persistent) - Prevent Sybil attacks without cost-of-entry (proof-of-funds or proof-of-work) - Encode subjective judgments (only objective facts)


Applications

CRT is suited for: - Long-term business relationships - Inheritance and intergenerational transfer - Decentralized marketplaces - Reputation-based access control - Coordination without institutions

CRT is NOT suited for: - Anonymous transactions (requires persistent identity) - Instant finality (Bitcoin confirmations take time) - Off-chain enforcement (only on-chain actions are observable) - Complex subjective disputes (requires human judgment)


Next Steps

See CRT in practice: Architecture

Understand time-locks: Time-Locked Covenants

Learn about reputation: Reputation & Incentives


CRT is a framework, not a solution.
It solves some problems by creating new constraints.