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- Problem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)Consider the game below: Player C Strategy C1 50, 50 Strategy C2 Strategy R1 Strategy R2 Player R 800, 800 1000, 1000 100, 100 Playing the game sequentially would result in C getting: 100 800 It depends if R plays first or second 50 1,000CNG Pipeline Company At the weekly brainstorming session, John Spychalski, president of CNG Pipeline Company (CNG), suggested that they build a new pipeline from Elizabeth, New Jersey, to the Midwest to move refined petroleum products, gasoline, and diesel fuel. Following some discussion, he asked the strategic planning group to consider the idea before the next brown-bag session. Skip Grenoble, vice president for strategic planning, thought that John was not con- sidering the cost and impact of this idea. How could CNG obtain land to build the pipe- line, let alone obtain the necessary capital to finance the project? Then there was the question of the existing refineries located in Ohio, Indiana, and Illinois. Skip knew refined petroleum products were being transported from the Gulf of Mexico refineries via barge and pipeline to the Midwest market areas currently. Skip turned over the project to Evelyn Thomchick, chief strategy analyst, to develop a preliminary analysis of the…
- 2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Animal A Hawk Dove (rows)/Animal B (columns) (-5,-5) (0,10) (10,0) (4,4) Hawk Dove An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share.5,3 4,4 3,6 7,6 Find the pure strategy nash equilibriaPlayer 2 Strategy A Strategy B Player 1 Strategy A 3, 3 2, 2 Strategy B 2, 2 1, 1 a) Is A an evolutionary stable strategy? How do you know? b) Is B an evolutionary stable strategy? How do you know? c) Is there any mixed strategy that places positive probability on B that could be an evolutionary stable strategy? How do you know?
- 24. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 8<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?Question 2 (3,2) P2 D (1,-1) A E P1 (0, 1) What is the Nash equilibrium of the game? * (a) (B; C, F) * (b) (A; C, F) * (c) (A; E, G) * (d) (B; D, F) * (e) (B; E, F) B F (2,3) P2 G (1,2)UI. In American football, the offense can either run the ball or pass the ball, whereas the defense can either anticipate (and prepare for) a run or anticipate (and prepare for) a pass. Assume that the expected payoffs (in yards) for the two teams on any given down are as follows: (a) (b) (c) (d) OFFENSE Run Pass Anticipate Run 1,-1 DEFENSE 9,-9 Anticipate Pass 5,-5 3, -3 Show that this game has no pure-strategy Nash equilibrium. Find the unique mixed-strategy Nash equilibrium of this game. Explain why the mixture used by the offense is different from the mixture used by the defense. How many yards is the offense expected to gain per down in equilibrium?
- If a team from Trilogox came up with the following PFMEA exercise results during its risk exposure analysis: Risk Occurrence Probably will occur Outcome Detection Financial Cost increase by Detection method has 30% medium effectiveness Marketing Probably will not Cost increase by Detection method has medium effectiveness Cost increase by Detection method has medium effectiveness Cost increase by Detection method has 2% occur Quality Probably will occur 40% Capability Probably will occur 10% medium effectiveness Materials Probably will occur Cost increase by Detection method has medium effectiveness Cost increase by Detection method has 10% Labor Probably will occur 40% medium effectiveness b. Which are the most critical risks by identifying the critical values? What actions do you recommend? Evaluate the risks by assigning one degree of leniency in their value.QUESTION (1) Consider the following game tree of a two-stage dynamic game. Write the players' information sets and their associated pure strategies. Also, show all the subgames. Find all subgame perfect Nash equilibria of the game. (a) (b) (c) Find all perfect Bayesian equilibria of the two games below by specifying the beliefs. (d) Compare outcomes in (b) and (c). Player 1 + 2 A 3 L Player 2 D U 3 0 R 0 8 0 D Player 2 U 2Player 1 R Player 3 Player 2 а Player 3 Player 3 (3) (:) () () G) (F) 1 4 2 7 (a) Solve the game by backward induction and verify that the strategies found by backward induction constitute a Nash equilibrium. (b) Identify all other pure strategy Nash equilibria of the game. (c) Argue that all Nash equilibria found in (b) do not satisfy the principle of sequential rationality.