Mobile　Edge　Computing　(MEC)　can　augment　the　capability　of　Internet　of　Things　(IoT)　mobile　devices　(MDs)　through　offloading　the　computation-intensive　tasks　to　their　adjacent　servers.　Synergistic　computation　offloading　among　MEC　servers　is　one　possible　solution　to　reduce　the　completion　time　of　system　during　peak　hours.　However,　due　to　the　large　number　of　servers　and　the　long　distance　between　base　stations　(BSs),　synchronizing　the　information　of　all　servers　takes　a　long　time,　which　is　not　applicable　to　the　fluctuant　environments.　Meanwhile,　each　server　from　different　BSs　is　typically　selfish　and　rational,　and　can　only　obtain　the　imperfect　information　from　its　adjacent　servers,　which　is　a　challenge　for　computation　offloading　among　servers　from　a　global　perspective.　This　article　proposes　a　game-based　computation　offloading　scheme　with　imperfect　information　in　multi-edge　environments.　First,　a　non-cooperative　game　with　imperfect　information　is　designed　to　analyze　the　complex　interactions　during　synergistic　computation　offloading　among　MEC　servers.　Second,　a　Synergistic　Balancing　Offloading　Algorithm　(SBOA)　through　distributed　decision-making　manner　to　obtain　the　optimal　offloading　decision　is　proposed,　which　guarantees　that　the　game　converges　to　a　Nash　Equilibrium　(NE)　point.　Extensive　simulation　results　reveal　the　fast　convergence　of　SBOA.　As　the　percentage　of　high-load　servers　rises　and　the　number　of　heavy　tasks　increases,　SBOA　performs　better　than　other　benchmark　algorithms　in　terms　of　timeliness,　effectiveness,　and　system　completion　time.　©　2024　IEEE.