Before revision:  As a result, we found that, even in the case with observation errors, the only strategy sets that enforce a liner payoff relationship are either ZD strategies or unconditional strategies  , which were numerically confirmed .
After revision:  As a result, we found that, even in the case with observation errors, the only strategy sets that enforce a liner payoff relationship are either ZD strategies or unconditional strategies and that no other strategies can enforce it , which were numerically confirmed .