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We develop a general equilibrium model of cryptocurrency to study a double spending prevention mechanism without payment confirmations. Agents trade cryptocurrency using a digital wallet, and the cryptocurrency system provides a means to verify a wallet's double spending history. Double spending can be prevented without payment confirmations under some conditions if a wallet has a good reputation for transaction history. As the difficulty of mining work increases, incentives for double spending decrease. We provide new insights into the properties of Bitcoin transaction fees, quantitatively assess the current Bitcoin system, and evaluate the welfare gain from fast transactions without payment confirmations.

A search‐theoretic model is constructed, where money and Bitcoin can be used as mediums of exchange. We investigate how each currency facilitates transactions and how they compete with each other. Quantitative analysis shows that welfare in an economy with both money and Bitcoin is lower than in a money‐only economy due to congestions in the confirmation of Bitcoin transactions and that the welfare gap between the two economies expands as inflation rises. Moreover, an increase in transaction fees for Bitcoin can increase welfare by reducing inefficient Bitcoin transactions.

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We develop a general equilibrium model of cryptocurrency to study the optimal design of a cryptocurrency system. Agents trade cryptocurrency using digital wallets, and the cryptocurrency system provides verification of a digital wallet's history of double spending attempts. Delaying the delivery of goods until payment information is confirmed in the blockchain prevents double spending. However, double spending can be prevented without a delivery lag under some conditions if a wallet has a good reputation in terms of its history of double spending attempts. In particular, as the difficulty of mining work rises, the incentive to engage in double spending with a good wallet decreases. We study the optimal design of the cryptocurrency system in terms of the difficulty of mining work and the supply of cryptocurrency and evaluate the welfare gain that would be captured if the current Bitcoin system adopted the optimal cryptocurrency system.

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