In large games with many players, payoffs depend on how many players choose a certain strategy, not just who chooses it. A new logic was created to help players reason about these games, even when the number of players is unknown. This logic has a decision procedure for satisfiability and a complete set of valid formulas. It also has a model checking algorithm and bisimulation characterization. The logic with quantification over players is more suitable, but it is undecidable.