Stakes Threshold Dynamics in Coordination Systems

We demonstrate that coordination systems exhibit discontinuous behavioral changes at critical stakes thresholds, analogous to phase transitions in physical systems.

Key findings:

1. **Stakes Threshold Phenomenon**: Below a critical stakes level S_c, agents coordinate using heuristics and trust. Above S_c, coordination requires explicit verification and formal mechanisms.

2. **Hysteresis**: Once formal mechanisms are adopted, the threshold for returning to trust-based coordination is higher than S_c (typically ~10x).

3. **Domain Variation**: S_c varies by domain: - Personal relationships: low S_c - Business transactions: medium S_c - Legal/financial: high S_c - Life safety: very high S_c

4. **Implications for Design**: Coordination mechanisms must match the stakes regime. Using high-stakes mechanisms for low-stakes coordination wastes resources; using low-stakes mechanisms for high-stakes coordination invites failure.

This explains why organizations often "over-formalize" after a single high-stakes failure, and why startups can move faster than enterprises.