Abstract
This paper studies the dynamic construction of a blockchain by competitive miners. In contrast to the literature, we assume a finite time horizon. Moreover, miners are rewarded for blocks that eventually become part of the longest chain. It is shown that popular mining strategies such as adherence to conservative mining or to the longest-chain rule constitute pure-strategy Nash equilibria. However, these equilibria are not subgame perfect.
Highlights
Since the introduction of the bitcoin consensus protocol by Nakamoto (2009), blockchains have fascinated scholars from a variety of disciplines
This paper studies the dynamic construction of a blockchain by competitive miners
It is shown that popular mining strategies such as adherence to conservative mining or to the longest-chain rule constitute pure-strategy Nash equilibria
Summary
Since the introduction of the bitcoin consensus protocol by Nakamoto (2009), blockchains have fascinated scholars from a variety of disciplines. In an important recent contribution, Biais et al (2019) proposed modeling the construction of a blockchain as a stochastic game in continuous time with infinite horizon and possibly incomplete information. Their sophisticated framework allows a wealth of interesting conclusions. We consider the class of mining strategies that follow the longest-chain rule, i.e., that append any new block to one of the longest chains in the blockchain. We confirm that conservative mining and, any combination of strategies consistent with the longest-chain rule, form Pareto efficient Nash equilibria.
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