This paper studies coin selection algorithms employed by UTXO-based blockchains, such as Bitcoin and Cardano. In particular it introduces a modified greedy algorithm. Its aim is to minimize the UTXO pool size and keeping the transaction fee low. The adjustment results in a substantial average decrease of approximately 85% in the UTXO pool size, with a marginal average transaction fee increase of only approximately 0.07%. This paper prompts a critical inquiry into the nature of this trade-off, raising the question of whether the balance achieved is indeed a trade-off or if the focus should be redirected towards further optimizing the conventional greedy algorithm.

On certain blockchains that use the proof-of-stake consensus mechanism, agents who validate transactions can set up pools that allow other agents to delegate their stake to earn higher returns. We study a version of the standard staking pool formation game in the presence of malicious agents, with an arbitrary distribution of stakes of honest agents. We establish existence and uniqueness of equilibria, how blockchain security can be maximized and how a leverage constraint impacts the functioning of the blockchain.