Collusion Attack Cost Analysis

Collusion Model

Assume k validators collude for malicious voting. Their joint utility is:

U_collusion = k·B - P_detect·k·α·Stake

Where:
- B is single-round collusion benefit
- P_detect is detection probability
- α·Stake is slashing amount

Detection Probability

Using statistical detection methods, P_detect's relationship with collusion scale:

P_detect(k, n) = 1 - (1 - k/n)^m

Where:
- n is total validator count
- m is number of observed tasks

Minimum Collusion Cost

C_collusion = argmin_k [k·α·Stake·P_detect(k,n)]

Theoretical analysis:
When n > 100, α = 1%, Stake = 10,000 USDC:
C_collusion > $100,000 (Far exceeds single-task benefit)

Conclusion: Collusion attacks are economically infeasible