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Suppose the buyer successfully solves the PoW for the block containing this alternative history. Note that the buyer has an option whether to broadcast the secretly mined block immediately or withhold it for future mining. If he decides to broadcast the block immediately, the seller will not receive the payment, but he will also not deliver the goods as shown on the top of the figure. Hence, the double-spending attack is not successful for the buyer. Alternatively, the buyer can temporarily withhold the solved block and continue to secretly mine another block (depicted on the bottom of the figure). Specifically, the buyer needs to allow other miners to confirm the original payment to the seller, so as to induce the seller to deliver the goods. At the same time, the buyer needs to secretly mine two blocks in a row for which the original transaction is removed.12 If the buyer is successful in mining two blocks faster than other miners, he can announce an alternative blockchain after the goods are delivered. In this case, the buyer gets the goods without paying the seller. More generally, if the seller delivers the goods only after observing N confirmations of the payment, the buyer needs to solve blocks N + 1 consecutive times in order to double spend successfully. To summarize, trust in a cryptocurrency system involves the interplay of three ideas: the security of the blockchain, the health of the mining ecosystem and the value of the currency.13 As shown in Figure 2.5, sufficient mining activities are required for ensuring the security of the blockchain, safeguarding it against attacks and dishonest behaviors. Moreover, only when users trust the security of system will the cryptocurrency be widely accepted and and traded at a high value. Finally, the value of the currency supports the reward scheme to incentivize miners to engage in costly mining activities. Our model will capture precisely this interdependence by explicitly looking at the joint determina- tion of mining efforts, rewards and cryptocurrency value in general equilibrium. The main features of a cryptocurrency model in Section 3 are therefore given by (i) a consensus protocol: miners compete to update a blockchain with the probability of winning being proportional to the fraction of computational power owned by a miner 12Since the consensus protocol prescribes that the longest chain is accepted by the miners, the double spender needs to mine two blocks in order to create an alternative, longer blockchain superseding the existing one which has one block solved already. 13This has been pointed out already in the computer science literature (see for example Narayanan et al. (2016)), but without making the connection to an equilibrium incentive problem for double spending. 10PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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