Topics in Game Theory — DU B.A. (Hons.) Economics Previous Year Question Papers

3. The question paper consists of two Sections: A and 8. 6. All parts of a question must be answered together. Q 1. Consider the following strategic form game between two players: Player 1 \ Player 2 X Y Determinethebestresponsefunctionsofboth!blayersandidentifytheNashequilibriumofthe game. Examine whether any strategy is strictly dominated. (6) Q2. Consider a sequential game in which Player 1 moves first and chooses between L and R. Player 2 observes the action chosen by Player 1 and then chooses between two possible actions at each decision node. Payoffs` 'ar`e as follows: Solve the game using backward induction and determine the Subgame Perfect Nash Equilibrium. Player 1 \ Player 2 Left Right Provide justification for your answer. (6) Q4. Explain the role of commitment in sequential games. How does the ability to commit to a particular course of action influence the strategic choices of other players? Discuss the impolfance of credible commitment in determining equilibrium outcomes with the help of suitable example. (6) Q5. Consider the following stage game: Cooperate Defect Discuss"whether cooperation can be sustained when this game is repeated infinitely. Explain the importance of future payoffs in sustaining equilibrium behaviour. (6) Q6. Consider a market in which two firms compete in quantities. Firm 1 acts as a leader and Firm 2 acts as a follower. Market demand is given by: Cost functions are: Q7. A potential entrant is considering entry into a market currently served by an incumbent firm. The entrant must decide whether to Enter or Stay Out. If entry occurs, the incumbent chooses whether to Fight or Accommodate the entrant. The payoff matrix is: Fight Accommodate Stay Out 0,2 0,2 Determine the Nash equilibrium of the game. Discuss whether the incumbent's threat to fight entry is credible. Explain how commitment may influence the strategic outcome. (20) Q8. Two firms compete simultaneously by choosing output levels. Market demand is given by: Cost.functionsar!;: Derive the reaction functions of both firms and determine the Coumot Nash equilibrium outputs. Calculate equilibrium price and proflts. Briefly explain the economic intuition behind the equilibrium outcome. (20) Q9. Discuss how education may serve as a signal of worker ability in labour markets. Distinguish between pooling equilibrium and separating equilibrium in this context and explain their economic implications. (20) Q 10. How repeated interaction may facilitate cooperation among firms in oligopolistic markets? Explain the role of trigger strategies and punishment mechanisms in sustaining collusive outcomes. (20) # ada ad (strictly dominated) ₩ı (6314) 398 Subme Perfect Nash Equilibrium pet (Cooperate) a14 (Defect) air (Defect) 8,1 3,3 zis a (Section B) = →Q=1+2 (Cost functions) #: C_1(9_1) = 30g_1 C_2(9_2) = 30q_2 $ (Fight) { (Accommodate) aTET T# (Stay Out) 10,2 10,2 ¡ < # {a < (trigger strategies) it d5 # (punishment mechanisms)