Choosing Objects Four objects , and have different worths for two players 1 and 2, given by the following table: Player 1 starts with choosing an object. After him player 2 chooses an object, then...

Choosing Objects

Four objects
, and

have different worths for two players 1 and 2, given by the following table:

Player 1 starts with choosing an object. After him player 2 chooses an object, then player 1 takes his second object, and finally player 2 gets the object that is left. The payoff for a player is the sum of the worths of the objects he obtains.

(a) Draw the decision tree for this extensive form game.

(b) How many strategies does each player have?

(c) Determine the backward induction or subgame perfect equilibria (in pure strategies). How many different subgame perfect equilibria are there? What are the associated outcomes, and the resulting divisions of the objects?

(d) Is there a Nash equilibrium in this game resulting in a division of the objects different from the division in a subgame perfect equilibrium?