Question

Represent the following strategic interactions using payoff matrix/matrices:

Three players are playing the following game: Each of them will put a penny (1 cent in the US) down simultaneously, each choosing between head and tail. If players 1's and 2's penny are on the same side (i.e., both heads or both tails), then player 1 takes over player 2's penny. If player 1's and 2's penny are mismatched (i.e., one head, one tail), player 2 takes over player 1's penny. If player 3 chooses the head, she gets the same payoff as player 1. If player 3 chooses tail, she gets the same payoff as player 2. Everyone prefers having more pennies to fewer pennies.

Answer 1

Three players are playing the game.

If players 1's and 2's penny are on the same side (i.e., both heads or both tails), then player 1 takes over player 2's penny. (Let’s assume in this case Player-1 will get Payoff “1” )

If player 1's and 2's penny are mismatched (i.e., one head, one tail), player 2 takes over player 1's penny. (Let’s assume in this case Player-2 will get Payoff “1” )

If player 3 chooses the head, she gets the same payoff as player 1. If player 3 chooses tail, she gets the same payoff as player 2. (Here the payoff obtained by the player-3 would be as per the question )