We study double-spending attacks in a digital payment system, such as cryptocurrency, wherein agents send transaction messages to facilitate the transfers of digital currencies. The system is imperfect such that the payer can send a double-spending message to transfer the currency to another account owned by herself after the original message is sent, and the payment system may recognize the double-spending message instead of the original one as the real transaction. If this occurs, the seller will not receive the payment, and the payer may retract the payment but keep the merchandise. We consider multiple mechanisms that can be applied to deter double-spending attempts, including a cost to send a message, a currency deposit, and currency deletions. However, applying the above mechanisms is costly. If the probability of detecting fraudulent activity is low, employing fraud deterrents may not be ideal, and allowing for double spending may instead reflect an optimal equilibrium.

我们研究了数字支付系统中的双花攻击，例如加密货币，其中代理商发送交易消息以促进数字货币的转移。该系统是不完善的，因此付款人可以在发送原始消息后发送双重支付消息以将货币转移到自己拥有的另一个帐户，并且支付系统可能会将双重支付消息而不是原始消息识别为该双重支付消息。真实交易。如果发生这种情况，卖方将不会收到付款，付款人可以撤回付款但保留商品。我们考虑了多种可用于阻止双重支出尝试的机制，包括发送消息的成本，货币存款和货币删除。但是，应用上述机制是昂贵的。