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Eyal and Sirer's selfish mining strategy has demonstrated that Bitcoin systemis not secure even if 50% of total mining power is held by altruistic miners.Since then, researchers have been investigating either to improve theefficiency of selfish mining, or how to defend against it, typically in asingle selfish miner setting. Yet there is no research on a selfish miningstrategies concurrently used by multiple miners in the system. Theeffectiveness of such selfish mining strategies and their required mining powerunder such multiple selfish miners setting remains unknown.  In this paper, a preliminary investigation and our findings of selfish miningstrategy used by multiple miners are reported. In addition, the conventionalmodel of Bitcoin system is slightly redesigned to tackle its shortcoming:namely, a concurrency of individual mining processes. Although a theoreticalanalysis of selfish mining strategy under this setting is yet to beestablished, the current findings based on simulations is promising and ofgreat interest. In particular, our work shows that a lower bound of powerthreshold required for selfish mining strategy decreases in proportion to anumber of selfish miners. Moreover, there exist Nash equilibria where allselfish miners in the system do not change to an honest mining strategy andsimultaneously earn their unfair amount of mining reward given that theyequally possess sufficiently large mining power. Lastly, our new model yields apower threshold for mounting selfish mining strategy slightly greater than onefrom the conventional model.

On the Preliminary Investigation of Selfish Mining Strategy with Multiple Selfish Miners