## Abstract

Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to capture miners’ incentives to invest in equipment. In our model, n miners compete for a prize of fixed size. Each miner chooses an investment q_{i}, incurring cost c_{i}q_{i}, and then receives reward (Formula presented.), for some α ≥ 1. When c_{i} = c_{j} for all i, j, and α = 1, there is a unique equilibrium where all miners invest equally. However, we prove that under seemingly mild deviations from this model, equilibrium outcomes become drastically more centralized. In particular, ▬ When costs are asymmetric, if miner i chooses to invest, then miner j has market share at least (Formula presented.). That is, if miner j has costs that are (e.g.) 20% lower than those of miner i, then miner j must control at least 20% of the total mining power. ▬ In the presence of economies of scale (α > 1), every market participant has a market share of at least (Formula presented.), implying that the market features at most (Formula presented.) miners in total. We discuss the implications of our results for the future design of cryptocurrencies. In particular, our work further motivates the study of protocols that minimize “orphaned” blocks, proof-of-stake protocols, and incentive compatible protocols.

Original language | English (US) |
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Title of host publication | 10th Innovations in Theoretical Computer Science, ITCS 2019 |

Editors | Avrim Blum |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770958 |

DOIs | |

State | Published - Jan 1 2019 |

Externally published | Yes |

Event | 10th Innovations in Theoretical Computer Science, ITCS 2019 - San Diego, United States Duration: Jan 10 2019 → Jan 12 2019 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 124 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 10th Innovations in Theoretical Computer Science, ITCS 2019 |
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Country/Territory | United States |

City | San Diego |

Period | 1/10/19 → 1/12/19 |

### Bibliographical note

Funding Information:Supported by NSF CCF-1717899.

Publisher Copyright:

© Nicholas Arnosti and S. Matthew Weinberg.

## Keywords

- Bitcoin
- Cryptocurrencies
- Rent-seeking competition