Problem
Consider the following situations where two players are to split $10.
I. First consider a simultaneous-move game in which each of the two players is asked to announce what he would want. The moves are simultaneous. If their announcements I and y add up to $10 or less, each gets what he announced. If they add up to more than $10, neither gets anything. What are the Nash equilibria of this game? Explain.
II. Now consider a sequential version of this game, where Player 1 is first to announce his proposed split of $10, z and (10 - 2), between himself and Player 2. Then Player 2 decides whether to accept or reject the offer. If accepted, the proposed split is realized; if rejected, neither player gets anything. What are the subgame perfect Nash equilibria of this game? Explain.
III. Experimental evidence suggests that real-world outcomes of the game de scribed in (II) are biased away from the subgame perfect Nash equilibrium prediction towards the 50-50 split. Does this mean that game theory is wrong? Explain. What other factors, not incorporated in your analysis in (II), may be important in determining the outcome of this game?