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What are the subgame perfect nash equilibria of the game

**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?

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## Q : Draw the extensive form of the game and find subgame perfect

Consider an entry game. First the entrant decides whether to enter. Draw the extensive form of the game and find the subgame perfect equilibrium.