Consider a game where two players take turns deciding whether or not to take a p

Question

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. Suppose when no players ever take the large pile of money that at the end of the game, rather than player 1 being awarded the large pile, both players are awarded an equal share of both piles of money. How does this change the outcome of the game?

Explanation / Answer

In such a situation, no player would take the large pile as both will feel it is a safer option to just get half the amount at the end instead of having a chance of losing everything.

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