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B Appendix [FOR ONLINE PUBLICATION ONLY] – A formal description of the blockchain Aggregate State Let mDt (i) ≥ 0 denote the cryptocurrency balance held by agent i in the period t day market. We then use StD = {mDt (i)} to denote the entire public record of the holdings of these balances, called the (aggregate) state. Similarly, mN (i) ≥ 0 and SN denote the balances and the state at t,n t,n the beginning of the nth trading session of the period t night market. The economy starts with a given initial state S0D. Payments Weuse∆Dt (i,j)and∆Nt,n(i,j)todenoterespectivelydayandnighttransfersofbalancesfromagent i to agent j and call these transfers payments. A day payment is feasible if ∆Dt (i,j)≥0, mDt (i)≥∆Dt (i,j). j Similarly, a night payment is feasible if ∆Nt,n(i, j) ≥ 0, mNt,n(i) ≥ ∆Nt,n(i, j). j An agent can pay positive amounts to others and the total payments are bounded by the balances one has accumulated.33 An agent’s balances accumulate over time as a result of net payment inflows. Therefore, given any payments, the state is updated in the two markets according to mNt,0(i)=mDt (i)+∆Dt (j,i)−∆Dt (i,j)+Tt(i), j mNt,n(i) = mNt,n−1(i) + ∆Nt,n−1(j, i) − ∆Nt,n−1(i, j), for n = 1, ..., N ̄ j mDt+1(i) = mNt,N ̄ (i) + ∆Nt,N ̄ (j, i) − ∆Nt,N ̄ (i, j) j (B.1) (B.2) (B.3) 33Through cryptography, the authenticity of payments is protected by digital signatures corresponding to the sending addresses. As a result, only the owner of the digital signature can transfer balances to another address. This gives rise to the non-negativity and the cash-in-advance constraints. 55PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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