At a large round table sit n ≥ 2 players, each holding 3 cards: one white, one black, and one red. Each player must secretly choose one of their cards and then, when the bell rings, simultaneously reveal it publicly with all the others. If all players choose the white card, each of them receives 6 points. If player i chooses the white card, and at least one of the other players chooses a card of a different color, player i receives 1 point. If player i chooses the black card, they receive 3 points, regardless of the decisions of the other players. If player i chooses the red card, they receive 0 points, regardless of the decisions of the other players. Find all symmetric Nash equilibria of the given game in strategic form.
At a large round table sit n ≥ 2 players, each holding 3 cards: one white, one black, and one red. Each player must secretly choose one of their cards and then, when the bell rings, simultaneously reveal it publicly with all the others. If all players choose the white card, each of them receives 6 points. If player i chooses the white card, and at least one of the other players chooses a card of a different color, player i receives 1 point. If player i chooses the black card, they receive 3 points, regardless of the decisions of the other players. If player i chooses the red card, they receive 0 points, regardless of the decisions of the other players. Find all symmetric Nash equilibria of the given game in strategic form.
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