### Game Theory Question

Here is one that my friend Paul and I were talking about:

Two Players

10 Rounds

Each round, Player 1 is given five dollars. He can elect to give Player 2 as much of the five dollars as he wants. For every dollar that 1 gives, 2 gets three bucks. Player 2 can then give back as much of the money as he wants. What is the equilibrium in this game? We used basic backwards induction and figured that Player 1 would keep the $5 every round. We aren't certain on this, however, and Paul says that he's read that our equilibrium doesn't hold in tests of this game.

Two Players

10 Rounds

Each round, Player 1 is given five dollars. He can elect to give Player 2 as much of the five dollars as he wants. For every dollar that 1 gives, 2 gets three bucks. Player 2 can then give back as much of the money as he wants. What is the equilibrium in this game? We used basic backwards induction and figured that Player 1 would keep the $5 every round. We aren't certain on this, however, and Paul says that he's read that our equilibrium doesn't hold in tests of this game.

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