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where T(i) denotes the potential transfers of new balances to agent i in the day market by the cryptocurrency system. Blockchain Due to public monitoring, feasible payments during the day automatically update the aggregate state according to the rule (B.1). The new state at the start of the night market is thus given by SN = ΨN (SD, BD) (B.4) t,0 0 t t where BtD = {∆Dt (i, j)} is the entire set of day transfers and is called a block. The update function ΨN0 is defined according to (B.1). Payments in the night market, however, enter the state through a process we call mining. When agent i makes a payment to agent j in the night, he needs to send out an instruction for a feasible payment ∆Nt,n(i,j) to a pool of miners who compete to update the state with a new block of feasible payments in session n of the night market. The set of feasible payment instructions BN = t,n {∆Nt,n(i,j)} is the nth block of period t payments in the night market. Asequenceofblocks{BD,{BN }N ̄ }T iterativelygeneratesasequenceofstates{SD,{SN }N ̄ }T+1 according to SN =ΨN(SD,BD) t,0 0 t t ), for n = 1,...,N ̄ where the update functions ΨNn ,ΨD are defined by (B.1)-(B.3). We call the sequence of blocks B = {BD , {BN }N ̄ }T a blockchain. Determined by the process of mining, one specific blockchain T t t,n n=0 t=0 is used to construct the public state and can be observed by everyone in the economy at all times. t t,n n=0 t=0 t t,n n=0 t=0 SN = ΨN(SN ,BN t,n n t,n−1 t,n−1 SD =ΨD(SN ,BN ), t+1 t,N ̄ t,N ̄ 56PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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