# Fight for a Dollar

Logic Level 4

Amy and Becca play a game in which they choose an amount to pay ($$A$$ and $$B,$$ respectively). These amounts determine each person's odds of winning the "prize pool" (i.e., Amy wins with odds $$A:B$$ and Becca wins with odds $$B:A$$).

The "prize pool" of this game is the sum of both of the payments plus an additional \$1. How big will the prize pool be if Amy and Becca play according to the pure-strategy Nash Equilibrium of this game?

Assume that they can pay any positive real number amount of money, and give your answer to 3 decimal places.

×