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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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