Problem Setup

How to set up a convex program to incentivize maximum qualified volume to prediction markets

Suppose we have n (up to 256) miners whose route volume on market positions through the Almanac app into a prediction market. When a miner creates a position of size V, Almanac takes a 1% protocol fee and records the remaining 99% as unqualified volume. For example, if a miner makes a $100 trade, $1 is retained by the protocol and $99 is logged as unqualified flow—that is, we only count qualified flow as positions that actually got the prediction right. Each miner’s trailing qualified volume is denoted V_i^prev, and these values form the raw input to our convex program. e.g. -> V_i^prev= [$13000, $6310, ... $580] -> An array of previous trading volume that won money We are then given a budget B alpha tokens to distribute each epoch via Bittensor emission. The job of the convex program then, is to allocate fractions x_i ∈ [0,1] of each miner’s qualified block V_i^prev such that the total reward distribution both respects budgetary limits and incentivizes miners to continue producing high quality signals. Formally for each miner i is the primary quantity we want to maximize. Greater routed qualified volume means more valuable conviction-weighted signal is flowing through Almanac into prediction markets. At the same time, each allocation comes with a payout cost c_i​x_i, in alpha tokens, which must fit within budget constraints. If the payouts are allocated and aligned with the best signals, top performers will enjoy a windfall and be incentivized to keep playing in the tournament under competitive pressure to perform. Note:

• c_i ​is a number like 0.13 which tells us the unit cost in alpha tokens we have to pay to get a unit of qualified volume from the miner i. If the miner is very good, this number will be higher because its more expensive to get them to provide the great data and vice versa. Ultimately you will see our optimization will minimize the c_i​'s in the end. But for now we are concerned with maxing out volume.

• Think of x_i as a value that explains the opportunity a miner i has to earn money based off past performance. It's like a promise to fund the miner's trades that is built up over time and they can choose to trade real capital this block and that potentially allocates them a piece of the budget B. If the miner is profitable this block, their share of the next budget allocation will grow a bit more and they will earn some alpha tokens.