Consider a game where two players take turns deciding whether or not to take a pile of money. At the start of the game, there are two piles of money, one "large" pile with 5 dollars and one "small" pile with 1 dollar. Player 1 gets to choose whether to take the large pile, or leave both piles alone.
- If player 1 takes the large pile, he receives 5 dollars as his payoff, and player 2 receives the small pile, 1 dollar, as his payoff, and the game ends.
- If player 1 leaves both piles alone, both the large and the small piles double (10 dollars, and 2 dollars, respectively)
- Player 2 then decides whether to take the large pile of leave both piles alone.
- Every time a player leaves both piles alone, both piles double in size.
- Players take turns deciding whether to take the large pile or leave the piles alone until each player has had three oppourtunites to take the large pile (six rounds total).
- If, at the end of the game, neither play has taken the large pile, player 1 is awarded the large pile (which will contain 320 dollars at this point) and player 2 is awarded the small pile (which will contain 64 dollars).
1. Label the best response at every stage of the game. What will the outcome of this game be?