The game-theory problems of PQ sunsetting modes

The exploration of game-theory problems in relation to post-quantum scenarios involving Bitcoin reveals various strategic considerations that could impact the security and economics of the blockchain. The "tripwire" scenario introduces a mechanism where a NUMS puzzle is embedded in a honeypot UTXO with Bitcoin rewards, designed to trigger a freeze on all legacy coins once solved by a quantum computing entity. This approach, while technically feasible, raises concerns about why a rational quantum computing entity would reveal its capabilities by solving such a publicly visible puzzle, thereby losing the opportunity to covertly transfer legacy coins to a secure wallet.

A more complex scenario involves a potential collusion between a 51% majority of miners and a quantum computing entity to prevent the inclusion of post-quantum proofs in the blockchain. This could enable the extraction of legacy P2Pk coins estimated to be worth $215 billion, representing a significant economic incentive for miners. The competition between two similarly capable quantum entities might lead miners to align with the one offering higher reorganization fees, thus shifting the strategic balance in favor of overt actions over covert extractions.

Additionally, the implementation of sunsetting measures like those outlined in BIP361, which proposes a flag-day activation, doesn't necessarily mitigate the risk of deep chain reorganizations prior to activation. Such strategies increase coordination costs and highlight information asymmetries regarding the timing of quantum breakthroughs, potentially allowing quantum entities to exploit these gaps.

The discussion extends to the overall implications for blockchain security and stability in the face of quantum advancements. Given the removal of checkpoints from Bitcoin software and the reliance on miner consensus, the network may become vulnerable to attacks by quantum-capable entities, particularly targeting legacy coins not upgraded to quantum-resistant formats. The potential rollback of the blockchain to pre-migration states poses a severe threat to both legacy and upgraded coins.

This analysis underscores the need for further research and development efforts to address the challenges posed by quantum computing to the Bitcoin network. The dynamics introduced by quantum capabilities necessitate a reevaluation of current security assumptions and the exploration of new defensive mechanisms to safeguard blockchain finality and integrity in a post-quantum world.