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3.1 Basic Set-up We begin our analysis by looking at a single transaction period. As shown in Figure 3.1, there are N ̄ + 1 subperiods within the single period. In subperiod 0, a buyer meets a seller to negotiate a trade. All other subperiods 1, . . . , N ̄ serve as periods for confirming and settling trades that take place in subperiod 0. seller negotiate (x, d, N) delivers x buyer sends d buyer double spends n=0 n=1 n=2 ... n=N ...n=N ̄ Figure 3.1: Timeline for a single transaction period The buyer carries a real balance of cryptocurrency equal to z that can be used to buy an amount of goods x from a seller. Upon being matched, the buyer and the seller bargain to determine the terms of trade (x, d, N ) which specify that the buyer pays the seller d ≤ z units of real balances and that the seller commits to deliver x units of goods after a number of successive payment confirmations N ∈ {0, . . . , N ̄ } in the Blockchain.14 We call N the confirmation lag of the transaction. For now, the terms of trade are taken as given, but will be determined endogenously in the next section. The seller produces the good at unit costs, while the buyer’s preference for consuming an amount x with confirmation lag N are given by δN u(x) (1) where δ ∈ (0, 1) is the discount factor between two subperiods. Hence, discounting across the whole transaction period is given by15 β = δN ̄+1. (2) Finally, both buyers and sellers value real balances linearly and discount all payoffs that arise after the single transaction period at β. 14We consider the case in which a seller can commit to deliver the good. If this were not the case, only spot trades can be conducted that – as we show later – will always be subject to double spending. 15There are two ways to interpret the discount factor δ: (i) buyers prefer earlier consumption or (ii) a buyer’s preference can change over time so that a seller’s goods will no longer generate utility with probability 1 − δ. 13PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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