In　this　article,　evolving　and　incremental　value　iteration　(VI)　frameworks　are　constructed　to　address　the　discrete-time　zero-sum　game　problem.　First,　the　evolving　scheme　means　that　the　closed-loop　system　is　regulated　by　using　the　evolving　policy　pair.　During　the　control　stage,　we　are　committed　to　establishing　the　stability　criterion　in　order　to　guarantee　the　availability　of　evolving　policy　pairs.　Second,　a　novel　incremental　VI　algorithm,　which　takes　the　historical　information　of　the　iterative　process　into　account,　is　developed　to　solve　the　regulation　and　tracking　problems　for　the　nonlinear　zero-sum　game.　Via　introducing　different　incremental　factors,　it　is　highlighted　that　we　can　adjust　the　convergence　rate　of　the　iterative　cost　function　sequence.　Finally,　two　simulation　examples,　including　linear　and　nonlinear　systems,　are　conducted　to　demonstrate　the　performance　and　the　validity　of　the　proposed　evolving　and　incremental　VI　schemes.