Staking Pools with Arbitrary Stake Distribution

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.