A ........... game is one in which it is not possible to commit to strategies.
Non-co-operative
Cooperative game: players can make binding agreements (enforceable commitments) about the strategies they will play.
Non-cooperative game: binding commitments are not possible, so each player chooses a strategy independently to maximise own payoff (for example, the prisoners' dilemma, solved by Nash equilibrium).
Zero sum describes the payoff structure (one player's gain equals the other's loss) and competitive is a general description; neither is defined by the absence of commitment.
So a game in which players cannot commit to strategies is a non-cooperative game.
Hence, Non-co-operative.
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