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The expected profit of a miner in equilibrium across the single transaction period is thus given by Πm =(N ̄ +1) Q βR−Q= N ̄ +1βR. (8) Mm=1 Q M2 To capture the fact that mining tends to be quite competitive and open to new entrants, we let M → ∞17 to arrive at the following lemma. Lemma 1. As M → ∞, the expected value of miners is zero, and the aggregate computing power of miners dissipates all rewards from mining MQ = βR. 3.3 Secret Mining As discussed in Section 2, an important concern in a cryptocurrency system is a buyer’s double spending attempts (see Property (ii) in Section 2). When trading, the buyer needs to make a payment d to the seller. To do so, he has to send out an instruction to miners to update the Blockchain with the transaction. However, this is insufficient to ensure that the seller receives a payment. A buyer can engage in secret mining by attempting to mine a block in which his payment did not occur.18 A seller can protect himself from not receiving the payment by waiting to deliver the goods until the payment has been incorporated into the blockchain. Such confirmation of the payment in the Blockchain however may still be not enough. A buyer can secretly mine a different Blockchain which could be released some periods after the seller has delivered the good replacing the original Blockchain.19 When such secret mining succeeds, the 17The total number of miners is estimated to be within the range of 5000 to 100,000 (https://goo.gl/TPFBvA). In addition, according to blockchain.info, there are altogether 14 mining pools that individually can account for at least 1% of the total hashrate. Finally, it is feasible for miners to use their existing mining capacities to mine different cryptocurrencies. For example, ASICs (Application-specific integrated circuits) manufactured for Bitcoin can be used to mine altcoins that use SHA-256 as the hashing algorithm (e.g., Namecoin and Peercoin). 18The secret mining can be done either by the buyer himself or by hiring a miner to mine a block with the instruction that the payment did not occur. 19Notice that, with such secret mining, the buyer cannot spend the balances of any other agent because, to spend other agents’ balances, one would need to obtain the digital signature of other agents. He can only (i) change the payment instructions of his own transaction and (ii) remove other payment instructions from being mined – and, hence, confirmed – in the block. Hence, in reality a buyer trying to double spend has to remove his own payment and all other payment instructions involving his original balance being spent. 15PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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