As the chain progresses, newly minted stake is being emitted at our ination rate in proportion to I = R T . Importantly, the gradient of the incentive function with respect to the stake is positive and super-linear at our inection point between the honest and dishonest graph. Notably, I 2 , this ensures that the amount of stake held by each sub-graph reect a non-linear change in their ination at the next iteration. S = 5 7 (12) Initially, since SA > 0.5 and SB < 0.5 the proportion of stake emitted in sub-graph A exceeds that in sub-graph B, and sub-graph As incentive grows super-linearly compared to B. The result is that the ratio of stake decreases the cabal must continually add stake to its sub-graph to maintain itself through time.

SB SA+SB We consider this proportion between the competing graphs under continuous ination. Converting to python code ... tau = 0.1 temp = 10 stake_A = 0.51 stake_B = 0.49 history = [] for block in range(100): total_stake = stake_A + stake_B trust_A = 1/(1 + math.exp(-(stake_A/total_stake 0.5) * temp)) trust_B = 1/(1 + math.exp(-(stake_B/total_stake 0.5) * temp)) ranks_A = stake_A ranks_B = stake_B incentive_A = ranks_A * trust_A incentive_B = ranks_B * trust_B total_incentive = incentive_A + incentive_B total_stake = stake_A + stake_B stake_A += tau * total_stake * incentive_A / total_incentive stake_B += tau * total_stake * incentive_B / total_incentive print (block, stake_B / (stake_A + stake_B))

>> block | size of cabal 0 0.4877323388820201 1 0.4849535784321247 2 0.4815511535094221 3 0.477389901500398 4 0.4723093486843246 5 0.46612224574620587 6 0.45861590847737577 7 0.44955887540065376 8 0.43871643745912897 9 0.42587900870651624 10 0.41090548935459825 ... 90 0.0002827251010618101 91 0.00025719653886131316 92 0.0002339730247373799 93 0.000212846436856568 94 0.00019362744329658293 95 0.0001761438058611274 96 0.00016023883697158944 97 0.00014576999582759936 98 0.00013260761127280887 99 0.00012063371993464691

11 Conclusion We have proposed an intelligence market which runs on a P2P network outside of a trusted environment. Crucially, the benchmark measures performance as representational-knowledge production using other intelligence systems to determine its value. The fact that this can be done in a collaborative 8 and high-resolution manner suggests that the benchmark could provide a better reward mechanism for the eld in general. To achieve this aim, the paper began with the denition of a P2P network composed of abstractly dened intelligence models. We showed how this framework allowed us to produce a ranking for each peer based on the cost to prune it from the network. Peers negotiated this score using a set of weights on a digital ledger. However, the system was incomplete without mechanisms that prevented participants from forming dishonest sub-graphs.