The goal of thispaper is to establish a general framework for “Consensus Game” thatcharacterizes the behavior of blockchain ecosystems, and to addressbehaviors of the “Mining Pool Gap Game”, that is, we first give thecharacterizing and interpreting the behavior of “ConsensusEquilibria”, and establishing and explaining the stability of theblockchain platform itself with the positive answer based on theexistence of consensus equilibrium through the new concept called“consensus game” in the presence of mining gap (game) behavior, here, the blockchain ecosystem where “Gap Game” is located refersto a mining platform based on the consensus principle of “Proof ofWork” (PoW) with longest chain rules (LCR) proposed by Nakamoto in2008. Specifically, this paper first establishes the existence ofgeneral consensus equilibrium and the corresponding stabilityresults for continuous operation of the blockchain ecosystem undergeneral incentive mechanism conditions, based on the consensus gameframework in the blockchain ecosystem. Then, combined with the threemain factors involved in “mining Bitcoin” work, including workcosts, reward mechanisms, and mining capabilities, from theperspective of mining miner (group) profits, it interprets andanalyzes the potential impact of different embedding scenarios onthe “gap game behavior” of mining miners (groups). The theoreticalresults and case analysis of this article indicate that by combiningappropriate incentive compatibility mechanisms for different miningscenarios, the concept of consensus game (equilibrium) can obtain orform a consistent explanation and interpretation of mining behaviorin different scenarios without simulation results of scenario data.In addition, we have reason to expect and believe that consensusgames, combined with factors related to mining (group) profits, canhelp us build appropriate incentive compatibility mechanisms. Bycharacterizing behaviors such as “interval behavior”, “branchingchains”, and “mining pool attacks”, we can support the healthydevelopment of the digital economy and promote the development ofbasic theories of consensus economics.
