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RE: What are the Nash Equilibria in the curation game?
sqrt( P + R ) + sqrt( P )
I think this should be weight = sqrt( P + R ) - sqrt( P )
I'm not 100% clear whether it's just that voter or the entire curation reward.
The weight of the individual votes is scaled down with the reverse auction system, but the total_weight is calculated without the reverse auction system. The rshares remain unchanged from the reverse auction system. This means that for posts with votes before 15 mins, the sum of the individual vote weights is less that the total_weight. Curation rewards (the STEEM-equivalent of 25% of all rshares) for the individual voters are then payed out with the fraction weight/total_weight, leaving a share of the curation rewards in the pool.
Fixed the plus to minus, thank you. Will have to figure out if more accurately modeling the 15 minute interval makes any difference.
While rewards are still pending, the weights do add up to 100% when you include the author-curate-reward % (which since HF20 goes back to the reward pool).
I guess you mean the weight-% and author-curate-reward-% values as shown on steemd? These values are calculated by the steemd website and are not directly part of the blockchain data. They are calculated from the individual vote weights in relation to the total vote weight and, to my understanding, the author-curate-reward % is exactly a result of the mismatch between the sum of the individual vote weights and the total weight.