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University of ArizonaDepartment of Economics ECON 431Games & DecisionsMidterm #2What’s your name? ………………………………………………….1. Consider the following extensive form game:AYes No B00 Reneg Pay A Accept-18 Reject 33 -20 (i) List all strategies of player B. (ii) How many subgames are there? Indicate by making circles in the figure. (iii) What is the backward induction solution? University of ArizonaDepartment of Economics Professor Dufwenbergsample (1. continued…)(iv) Find all subgame perfect equilibria. (v) Explain why "player 1 chooses No" is neither a strategy nor a strategy profile. (vi) Find a Nash equilibrium which is not a subgame perfect equilibrium. (vii) Find a strategy profile which is not a Nash equilibrium. University of ArizonaDepartment of Economics Professor Dufwenbergsample 2. Consider the following game: 1Out In1L 30 R2 L 51 R L 00 00 R 15 (i) Does the game have perfect information or imperfect information? Explain. (ii) How many subgames are there? Indicate by making circles in the figure. (iii) Find all subgame perfect equilibria in pure strategies. University of ArizonaDepartment of Economics Professor Dufwenbergsample 4. Ann and Bob are going to split $10. They have agreed to the following rules. Ann firstdivides the money into two piles: $x in one pile and $10-x in the other pile, where x = 0,1, 2, 3, 4, or 5. Bob observes Ann’s division and then chooses which one of the two pileshe will get; Ann gets the remaining pile.(i) Model this situation as an extensive form game. (ii) Count the number of strategies for each player. (iii) Find all subgame perfect equilibria by using backward induction. (iv) Does the game have a pure strategy Nash equilibrium which is not a subgame perfectequilibrium? If so, describe it. If not so, prove it. [Don’t write down the normal form ofthe game. Just reason with reference to the extensive form!] University of ArizonaDepartment of Economics Professor Dufwenbergsample 5. BONUS QUESTION“All subgame perfect equilibria are Nash equilibria.” Is that claim true or false? If it istrue, explain why so. If it is false, prove this point by constructing a counterexample tothe claim (i.e. a game in which there is a subgame perfect equilibrium which is not aNash equilibrium).

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