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Problems 1 Consider an infinite repetition of the game below, and consider the following strategy, to...
For each of the following normal-form game below, find the rationalizable strategy profiles, using IENBRS, Iterated Elimination of Never a Best Response Strategies. (1)/(2) L C R (3,2) (4,0) (1,1) (2,0) (3,3) (0,0) (1,1) (0,2) (2,3)
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
Problems 3,4 and 5 Problem 3. Consider the game below. (a) There are no dominant or dominated strategies. Is there anything you can say about what players will do? Player 2 C T (2,1) (0,2) M (1,1) (1,1)| (1,0) B(0,1) (2,0) (2,2) (0,3) Player (b) Report the best responses Problem 4. Bertrand Competition With Different Costs Suppose two firms facing a demand Dip) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost e and Firm...
Consider the normal form game G. L C R T (0,0) (4,0) (-3,0) M (0,4) (2,2) (-2,0) B (0,-3) (0,-2) (-4,-4) Let G∞(δ) denote the game in which the game G is played by the same players at times 0, 1, 2, 3, ... and payoff streams are evaluated using the com- mon discount factor δ ∈ (0, 1). a. Find the minimal value of δ for which playing (M,C) is sustained as a SPNE via Grim-Trigger (Nash reversion). b....
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
S5. Consider the following game table: COLIN North South East West Earth 1,3 3,1 0,2 1,1 Water 1,2 1,2 2,3 1,1 ROWENA Wind 3,2 2,1 1,3 0,3 Fire 2,0 3,0 1,1 2,2 124 [CH. 4] SIMULTANEOUS-MOVE GAMES: DISCRETE STRATEGIES (a) Does either Rowena or Colin have a dominant strategy? Explain why or why not. (b) Use iterated elimination of dominated strategies to reduce the game as much as possible. Give the order in which the eliminations occur and give the...
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
Exercise 2. Consider the following perfect information game: 1,1 0,0 0,0 (i) Solve the game using backwards induction. (ii) Find the normal form representation of the game. (iii) Compute the set of admissible equilibria.
Consider the stage game below, and suppose it is repeated infinitely many times Player 2 D EF A 1,1 1,1 1,1 Player I B 1,8 7,5 1,1 C 5,7 8,3 1,1 To sustain a SPNE in which players play (C,E) in every period by means of a trigger strategy, the discount rate must be larger than or equal to C. 1/3 d. (CE) cannot be part of a SPNE.
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W Z X y a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 с Find all the Nash equilibria in the game in pure strategies.