general media Lex Luthor vs Batman

[Fractured 2,684]

After enough failures, Gotham city's had enough of their rodent problem. Instead of relying on the general incompetence of the police force, they hire someone who gets results.
Rules:
The fight takes place all over Gotham. Both characters know each others general strategies, but nothing specific. Lex Luthor is not allowed to harm any civilians as a by-product of this fight, so the flashier power suits and objects of mass destruction stay home. He gets a week to prepare. Batman, being his usual self, knows who coming for him almost immediately, and he gets a week of preparation as well. Lex starts the play by being air dropped in the middle of Gotham.