There's some handwaving about trust. They claim resistance against Sybil attacks, which is the biggest problem in anonymous distributed systems. That's where someone creates large numbers of phony identities to spam email, create link farms, and abuse reputation systems. If they could actually do that, they'd have a huge win. It's the basic reason P2P systems fail. They have a paper on how they do that, "On the Sybil-Proofness of Accounting Mechanisms in P2P Networks"[1] That's more important than this paper.
The other paper is analyzing Tribler, which is like BitTorrent. "Agents gossip about their transaction partners and inform others about their trustworthiness. Agents’ respective transaction histories are disseminated along the network. From this information agents can aggregate an approximation of their peers’ reputations such that free riders and otherwise uncooperative agents can be identified." Much of this is aimed at balancing the "seeders" and "leechers" of a file-sharing system.
Their TrustChain system is a more distributed blockchain-like system. Everybody has some chained blocks, and there's overlap, but nobody has all of them. The goal seems to be that most forgery is detected, but not all of it. In exchange for being only approximate, the system goes faster, uses less storage, and scales bigger.
All this is buildup to addressing the question of whether a group of nodes can cooperate to increase their reputation. The Sybil paper is a whole thesis on this, and heavy going. They're trying for a graph theory result.
I'm not clear on this, but the crux of the argument seems to be that in the seeder/leecher scenario, they can create a system where the cost of faking being a good seeder is higher than the cost of being one. This seems to depend on a cost metric which is internal to the network. If the benefit to the attacker is outside the network (sales from spams, higher reputation for a product or candidate), this might not work.
Good ideas there. They don't claim to have solved the general case, but they're trying.
[1] https://repository.tudelft.nl/islandora/object/uuid%3A6b4011...