Each day, you and a friend play odds/evens to see who gets the last doughnut. On

Question

Each day, you and a friend play odds/evens to see who gets the last doughnut. On command, you each extend either one or two fingers. If the sum of the fingers is odd, you get the doughnut. If the sum of the fingers is even, your friend gets the doughnut.
Let the payoffs from winning be 1, and from losing, 0. Fill in the payoff matrix below and answer the following question:



In a mixed-strategy equilibrium, what happens? A. You and your friend both play 1 finger less frequently than you play 2 fingers, and you expect to win more than 50% of the time. B. You and your friend both play 1 finger 50% of the time and 2 fingers 50% of the time, and you expect to win 50% of the time. C. You and your friend both play 1 finger more frequently than you play 2 fingers, and you expect to win more than 50% of the time.

Explanation / Answer

In case of one finger one finger case, friend will one and "you" will loose. So 1 is return and 0 is return of you. This is how table will be read.

B. You and your friend both play 1 finger 50% of the time and 2 fingers 50% of the time, and you expect to win 50% of the time.

Because there is 50% chances if you choose one finger you will win and 50% probability that you will loose. Same goes for ur friend . That's why b is the correct answer

You One finger Two finger Friend One finger (1,0) (0,1) Two finger (0,1) (1,0)

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