Game Theory and Strategic Interactions — DU B.A. (Hons.) Economics Previous Year Question Papers

Kalkaji, New Delhi-110019 Section A CGiR 6) l. (a) Consider the following normal form game between Player I and Player 2 : Player l\Player 2 x Y (i) Write down the best response functions for both players and represent them graphically on a best response diagram. Does the game have any pure strategy Nash Equilibrium (NE)? Justify your answer. (8) (ii) Define strictly dominated and weakly dominated strategies. Identify any dominated actions for each player, if any, and eliminate them systematically (if possible). Find the mixed strategy Nash Equilibrium (MNE) of the game, if it exists. Show all necessary calculations and reasoning. (12) (b) Consider a scenario in which a technology start-up (TS) is contemplating a strategic partnership with a large, established firm (L) in the same industry. Firm L may be one of two types: a Friend (F), genuinely interested in a mutually beneficial collaboration, or an Enemy (E), whose objective is to extract trade secrets for its own competitive advantage. Firm L knows its own type, but TS does not; it assigns equal probability to each possibility. Prior to any information exchange, firm L chooses an action: either to Invest (t), signalling a commitment to the partnership, or to Sabotage (S), indicating an exploitative motive. Simultaneously, the start-up chooses whether to Reveal (R) or Hide (H) its proprietary technology. The resulting payoffs depend on the type of the large firm and the combination of strategies chosen. The extensive form of the game is given below : Draw the Bayesian normal form matrix of this game. LOOS a ta dete te te te tae te pyge youe te bere ta t tan tan tan ta ta ta tan tan tan ta t to ton tacà Section B csc c) 2. Two players simultaneously and independently decide how much to contribute to a public good. If player I contributes x, and player 2 contributes x, then they both receive the value of the public good given by 2(x, + x, + x,xr). Assume that x, and x, are positive numbers. Player 1 must pay a cost x,2 of contributing; thus, player 1's payoff is u, : 2(x, * x, * x,xr) - x,2. Player 2 pays the cost t x22 so player 2's payoff is u, : 2(x, + x2 + xrx2) - txr2. The number t is private information to player 2. Player 1 knows that t equals 2 and 3 with equal probability. (i) Calculate the best response functions of player I and the two types of player 2. fl2) (ii) Compute the Bayesian Nash equilibrium and corresponding payoffs of this game. (8) 3. Consider the following extensive form representation of a game : (i) What conditions on c guarantee the existence of a separating perfect Bayesian equilibrium? Describe such an equilibrium. (10) (ii) For what values of c is there a pooling equilibrium in which both types of W choose O? Describe such an equilibrium. (10) 4. (a) Show that a player's bid equal to her valuation dominates all her other bids in a second price sealed bid auction with imperfect information about valuations. (5)