I think of bitcoin as a self-securing system. Value is created by solving the security problem of verifying the last block of bitcoin transactions. This verification serves as a decentralized stamp of approval, and the verification step consists of hashing a nonce and a block of transactions through a one way hash function and arriving at a checksum with a certain structure (which is hard because hash is random and meeting the structure requirement is a low probability event).
What happens if parties collude to get greater hashing power and increase their share of mining ? This is what happened with GPU mining farms on bitcoin. It was one of the motivations behind Ethereum, which enables code to run as part of transactions, and for the hashing algorithm to be not easily parallelized over a GPU. But it is not economical to mine on desktops as the motivation seems to suggest.
The important aspect I think is the self-securing idea – how can a set of computational systems be designed so that they are incentivized to cooperate and become more secure as a result of that cooperation.
At a recent blockchain conference, some interesting topics of discussion were zero knowledge proofs, consensus algorithms, greater network-member-ownership in a network with network-effects instead of a centralized rent collection, game theoretic system designs and various etherereum blockchain applications.