Question

Consider the international game of Rock-paper-scissors (also known around the world as scissors paper-stone, jan-ken-pon, ro-sham-bo, ching-chang-wulla, ka-chee-poon etc). Remember that scissors wins paper wins stone wins scissors (who can forget that!). If loser pays winner $c then

(A) there is no minimax

(B) scissors is minimax

(C) all three actions: rock, paper, scissors are minimax

(D) paper is minimax

(E) rock is minimax

Answer 1

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Answer:

All three actions are minimax as

If we analyze how the players choose their mixed strategies, we can see if we allow the players to go in order, and suppose that Player 2 chooses a strategy y first, then Player 1 will mix his strategies so as to maximize his payoffs, and thus choose the vector x that optimizes maxx? Ay. Knowing this, Player 2, who goes first will choose a vector y that minimizes this payoff Player 1 gets, and thus chooses the vector that optimizes

There are equal probabilities for both the players to choose three options predicting other outcome. Thus all the three actions have equal chances thus making it a zero sum game called hence minimax