The Economics of Proof-of-Useful-Work

Proof-of-work (PoW) blockchains rely on computational expenditure to secure a ledger supporting a native cryptocurrency. In existing systems such as Bitcoin, this expenditure is intentionally useless: the computation secures consensus but produces no external economic output. An emerging alternative -- proof of useful work (PoUW) -- enables the same computation to simultaneously secure the blockchain and generate economically valuable output. However, PoUW is often criticized on economic grounds: if the work is useful, attackers might be "paid to attack," potentially weakening security. We develop a competitive-equilibrium model of a PoUW blockchain in which compute can be allocated across pure mining, pure useful work -- instantiated as machine-learning inference -- or "duplex" work that produces both with computational overheads. We provide a complete closed-form characterization of equilibrium allocations and prices as a function of the duplex overheads and a single economic parameter -- the token-inference ratio -- measuring token adoption relative to the inference market. This characterization reveals three regimes: "Bitconia," in which the economy reduces to classical PoW; "Fortessia," in which duplex replaces mining, increasing security while useful output remains unchanged; and "Duplexia," in which token rewards subsidize inference, lowering prices and expanding inference supply. Contrary to the common strawman argument, PoUW does not make attacks economically cheap: once equilibrium prices are taken into account, the economic cost of a majority attack remains tied to the block reward. Moreover, in Duplexia, block rewards act as rebates on inference prices, generating additional socially useful computation that would not arise without the blockchain -- an expansion monotonically increasing in token adoption and technological efficiency.