Marine protected areas (MPAs) in the Southern Ocean are essential tools for marine conservation and Antarctic governance, yet new MPA proposals under CCAMLR have long struggled to become formal institutional outputs. This study conceptualizes this gridlock as an “institutional anti-commons”: under CCAMLR’s consensus rule, heterogeneous participating members possess de facto blocking capacity, while unresolved reservations may weaken the stability and implementation basis of agreement. To examine this explanation, we develop an institutional anti-commons framework and examine it through an agent-based evolutionary game model embedded in multiplex interaction networks. The model represents the 26 sovereign-state members of CCAMLR and distinguishes scientific participation, facility exposure, commercial fishery interest, sovereignty identity, and economic capacity. It compares a binary support–objection model with a conditional-support negotiation model, operationalizes agreement through a no-explicit-objection criterion, and evaluates transfer, pre-decision coordination, and network-layer specifications. Mechanism comparison shows that supporter-maintenance transfer alone has difficulty breaking gridlock, whereas interaction coordination more effectively reduces explicit objection. This study extends anti-commons theory to institutional decision-making and offers a diagnostic framework for understanding delays in institutional innovation in high-threshold international environmental regimes.