P2share: how to turn any network (or testnet!) into a bitcoin miner

In the realm of cryptocurrency mining, particularly within a sharechain model, concerns regarding the unfair advantage early miners may receive due to non-linear share issuance have been raised. A linear "work-for-shares" model is proposed as a solution to these concerns, ensuring that shares are issued in a manner directly proportional to the work contributed by miners. This approach eliminates the possibility of early miners gaining a disproportionate amount of shares, thereby preventing them from overshadowing new entrants in terms of competitiveness. The linear model relies on a difficulty adjustment algorithm designed to maintain fairness across all mining activities.

The concept of being paid multiple times for the same unit of work does not hold in this refined linear model, since the introduction of new shares through work continuously dilutes the value of all existing shares. This ensures that each share, regardless of its creation time, holds the same expected value over time. Thus, no enduring advantage is conferred upon early work, addressing the issue of potential unfairness in share distribution and valuation.

Miners make decisions based on the expected satoshis per unit hash on both the sharechain (EV_sc) and the mainchain (EV_mc), with the share price at which EV_sc = EV_mc denoted as P*. Their actions are guided by simple arbitrage principles: if EV_sc > EV_mc, mining efforts are directed towards the sharechain; if EV_sc < EV_mc, the mainchain is preferred; and if EV_sc is approximately equal to EV_mc, miners remain indifferent. Similarly, trading decisions hinge on the market share price in relation to P*: selling shares when the price is deemed "too high," buying more shares when the price is "too low," and remaining indifferent when the price is "just right." This framework ensures that all shares maintain equal expected value, promoting a fair and balanced mining ecosystem where strategic decisions are made based on objective evaluations of expected value and market price deviations.