Verifier's Dilemma Explainer

In recent years, Layer 2 blockchains have made significant progress, greatly benefiting the L1 ecosystems of both Ethereum and Bitcoin. Innovators like Arbitrum and Optimism have pioneered the OP Rollup. They cleverly designed a system to have one party do some work and escrow a bond to incentivize correct behavior, then invite others to challenge their work and take or ‘slash’ their bonded tokens if they catch the asserter cheating. Indeed, this system is simple and effective and dominates the Layer 2 space.

Unfortunately, you may notice that OP Rollups suffer from the Verifiers' Dilemma, which is the observation that there’s no point in checking somebody’s work if you know they’re not going to cheat; but if you’re not going to check, then they have a stronger incentive to cheat.

A Super-Simple Model

Consider a simple model with two players: the Asserter, who makes a claim that could be true or false, and the Checker, who can either verify the claim or do nothing, assuming the claim is true. Checking costs the Checker CCC, and they receive a reward RRR if they catch the Asserter cheating. If the Asserter cheats without detection, the Checker suffers a loss LLL.

Two Main Threats: Bribery and Laziness

1. Bribery: The Asserter might bribe the Checker to avoid verification. To prevent this, the Asserter must escrow a large deposit, more than the total value at stake, payable to the Checker if cheating is detected. This makes bribery economically unviable but requires full collateralization, which is expensive.

2. Laziness: The Checker might decide not to check the Asserter's work. The Checker's incentives can be analyzed as follows:

   • If the Asserter cheats with probability XXX, the Checker's utility is:

     • If checking: R×X−CR \times X - CR×X−C

     • If not checking: −X×L-X \times L−X×L

   • Checking is only worthwhile if X>CR+LX > \frac{C}{R + L}X>R+LC​. If the Asserter cheats randomly with a probability less than this threshold, a rational Checker will never check, allowing the Asserter to cheat without detection.

Numerical Example

Suppose checking costs $0.10 per transaction, the reward for catching cheating is $75, and the loss from undetected cheating is $25. The Asserter can cheat up to 1 in 1,000 times without detection. For a system running thousands of transactions, this poses a significant problem. Over-collateralizing the system can help but does not eliminate the risk entirely.

Multiple Checkers

Adding more Checkers does not necessarily help. With two Checkers, each independently deciding to check, the reward RRR might be split between them, reducing the expected reward and increasing the probability of undetected cheating. The problem worsens with more Checkers, as they have to split the reward multiple ways, reducing the incentive to check.

Are You Sure Your System is Incentive-Compatible?

For a system to be truly incentive-compatible, designers need to ensure that Checkers will verify claims even if they believe cheating is unlikely. Simply having a big penalty for cheating, a reward for catching cheaters, or many Checkers is insufficient and can sometimes make things worse.

The Way Out

AuditX’s dePIN x AI nodes perform continuous audits on registered Layer2 root states to confirm the assertions are correct and to earn rewards for strengthening on-chain security and transparency.