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

1. (a) Consider the following lobbying game between two firms. Each firm may lobby the government in hopes of persuading it to make a decision that is favourable to the firm. The two firms, X and Y, independently and simultaneously decide whether to lobby (L) or not (N). Lobbying entails a cost of 15. Not lobbying costs nothing. If both firms lobby or neither firm lobbies, then the government takes a neutral decision, which yields 10 to both firms. If firm Y lobbies and X does not lobby, then the government makes a decision that favours firm Y, yielding zero to firm X and 30 to firm Y. Finalty, if firm X.lobbies and Y does not, the government makes decision in favour ofX which yields 40 to firm X and zero to firm Y. The normal form of this game is: (i) Define Nash Equilibrium. Compute the pure-strategy Nash equilibrium of this game. (5) (ii) Compute the mixed-strategy Nash equilibrium of this game. (10) For the game tree above, answer the following questions : (i) Write down the strategy sets of each player. (ii) Write the above game in its normal form and find all Nash equilibria. (5) (iii) Find the subgame perfect Nash equilibrium of this game (5) (a) Differentiate between strictly and weekly dominated strategy in a normal-form game? (5) (b) Two players simultaneously throw their right arms up and down to the count of "one, two, three." On the count of three, each player quickly forms his or her hand into the shape of either a rock, a piece of paper, or a pair of scissors. Abbreviate these shapes as R, P, and S, respectively. The players make this choice at the same time. If the players pick the same shape, then the game ends in a tie. Otherwise, one of the players wins and the other loses. The winner is determined by the following rule: rock beats scissors, scissors beat paper, and paper beats rock. Each player obtains a payoff of 1 if he or she wins, -1 if he or she loses, and 0 if he or she ties. (i) Represent this game in the normal form i.e. specify set of players, set ofactions, preferences, and payoff matrix. (10) (ii) Does the game has any pure strategy equilibria? (5) Two players play a game in which each has three possible strategies. player I has to choose from Top (T), Middle (M), and Bottom (B), while player 2 has to choose froin Left (L), Centre (C), and Right (R). Their payoffs are given in the following table : (i) Write the best response functions and represent in a dot-circle graph. Does the game has any pure-strategy Nash equilibrium? (ii) Does either player have a strategy that is strictly dominated by another? If so which one? (5) (iii) After removing the strategies that are strictly dominated, find the mixed strategy Nash equilibrium of the game. (5) (b) In second price sealed bid auction, suppose vi denotes value player i attaches sealed bid bi. Justify whether (b,, br, ...., b,) : (v,, vr,......, v.) is a Nash 4. Consider a duopoly with the inverse demand curve P : 200 - 2Q, where