Population-Independent Pairwise Proportionally Imitative Dynamics for Multipopulation Games

Machida, Manao; Kanazawa, Takafumi

doi:10.1109/smc.2015.157

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…The growth rate of the miner population in a pool can be described by the replicator dynamics [44]. Based on the pairwise proportional imitation protocol [45], the replicator dynamics of pool i is given by the following Ordinary Differential Equation (ODE):…”

Section: Replicator Dynamicsmentioning

confidence: 99%

Mining Pool Selection under Block WithHolding Attack

et al. 2021

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In current Proof-of-Work (PoW) blockchain systems, miners usually form mining pools to compete with other pools/miners in the mining competition. Forming pools can give miners steady revenues but will introduce two critical issues. One is mining pool selection, where miners select the pools to join in order to maximize their revenues. The other is a Block WithHolding (BWH) attack, where pools can inject part of their hash/mining power into other pools to obtain additional revenues without contributing to the mining process of the attacked pools. Reasoning that the BWH attack will have significant impacts on the pool selection, we therefore investigate the mining pool selection issue in the presence of a BWH attack in this paper. In particular, we model the pool selection process of miners as an evolutionary game and find the Evolutionarily Stable States (ESSs) of the game (i.e., stable pool population states) as the solutions. Previous studies investigated this problem from the perspective of pool managers and neglected the revenues from attacked pools (attacking revenues), leading to less accurate and insightful findings. This paper, however, focuses on the payoffs of miners and carefully takes the attacking revenues into consideration. To demonstrate how the problem is solved, we consider the scenario with two mining pools and further investigate the case where one pool attacks the other and the case where the two pools attack each other. The results in this paper show that pools can attract more miners to join by launching a BWH attack and the attack power significantly affects the stable pool populations.

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Section: Replicator Dynamicsmentioning

confidence: 99%