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Problem of Nash Equilibrium

Carlos and Ivana are room-mates and friends. Carlos and Ivana eat together despite who cooks on a given night. Within this payoff matrix, Nash equilibrium could never be obtained in 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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