In　this　paper,　we　provide　a　new　theoretical　framework　of　pyramid　Markov　processes　to　solve　some　open　and　fundamental　problems　of　blockchain　selfish　mining　under　a　rigorous　mathematical　setting.　We　first　describe　a　more　general　model　of　blockchain　selfish　mining　with　both　a　two-block　leading　competitive　criterion　and　a　new　economic　incentive　mechanism.　Then　we　establish　a　pyramid　Markov　process　and　show　that　it　is　irreducible　and　positive　recurrent,　and　its　stationary　probability　vector　is　matrix-geometric　with　an　explicitly　representable　rate　matrix.　Also,　we　use　the　stationary　probability　vector　to　study　the　influence　of　orphan　blocks　on　the　waste　of　computing　resource.　Next,　we　set　up　a　pyramid　Markov　reward　process　to　investigate　the　long-run　average　mining　profits　of　the　honest　and　dishonest　mining　pools,　respectively.　As　a　by-product,　we　build　one-dimensional　Markov　reward　processes　and　provide　some　new　interesting　interpretation　on　the　Markov　chain　and　the　revenue　analysis　reported　in　the　seminal　work　by　Eyal　and　Sirer　(2014).　Note　that　the　pyramid　Markov　(reward)　processes　can　open　up　a　new　avenue　in　the　study　of　blockchain　selfish　mining.　Thus　we　hope　that　the　methodology　and　results　developed　in　this　paper　shed　light　on　the　blockchain　selfish　mining　such　that　a　series　of　promising　research　can　be　developed　potentially.