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Problem regarding to First Mover Advantage

Carlos and Ivana both are roommates and friends. Carlos and Ivana eat together regardless of who cooks. When this game is repeated almost daily, and on Thursday, Ivana is permitted to pick first, the probable result is that: (w) neither Carlos nor Ivana cook, nor do they eat. (x) Carlos alone cooks for both of them. (y) Ivana alone cooks for both of them. (z) Carlos and Ivana share the cooking chores, and after that they eat together.

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How can I solve my Economics problem? Please suggest me the correct answer.

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