Microeconomics (2nd Edition) (Pearson Series in Economics)
2nd Edition
ISBN: 9780134492049
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Chapter 13, Problem 8Q
To determine
Situations where a player chooses to play mixed strategy, if dominant strategy is given.
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Game Theory
Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be?
Note:-
Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
You will get up vote for sure.
Consider a normal form game in which player 1 has three strategies, A1, B1, C1
and player 2 has three strategies, A2, B2, C2. Suppose that A1 is a best response to B2, B1 is a best
response to A2, A2 is a best response to B1, and B2 is a best response to A1. Do we know with
certainty whether A1 is rationalizable or not?
With what probability does player 1 play Down in the mixed strategy Nash equilibrium? (Input your
answer as a decimal to the nearest hundredth, for example: 0.14, 0.56, or 0.87).
PLAYER 1
Up
Down
PLAYER 2
Left
97,95
47, 33
Right
8,43
68,91
Chapter 13 Solutions
Microeconomics (2nd Edition) (Pearson Series in Economics)
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- W X Y Z 47, 15| 39, 41 45, 53 12, 56 In equilibrium, what is the probability that player 1 will use the pure strategy X in this game?arrow_forwardIf the players play pure strategies, the game has no Nash equilibrium. But what if they choose their moves randomly? Let each player instead opt for a mixed strategy instead of a pure strategy. The first will play action Z with probability p, and the second will play action L with probability q. At which pair (p, q) are the mixed strategies of the players in equilibrium? At which pair (p, q) does neither player want to change strategy? When are both strategies simultaneously the best response?arrow_forwardConsider a normal form game in which player 1 has two strategies, A1,B1 and player 2 has two strategies, A2,B2. Suppose that A1 is a best response to A2 and A2 is a best response to A1. Do we know whether A1 is rationalizable?arrow_forward
- Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true? This is a game where players A and B have the same number of strategies. Player A will get a higher payoff than player B as A moves first. This is game will only have one Nash equilibrium. This is a game of perfect information.arrow_forwardDescribe the game and find all Nash equilibria in the following situation: Each of two players chooses a non-negative number. In the choice (a1, a2), the payoff of the first player is equal to a1(a2 - a1), and the payoff of the second player is equal to a2(1 – a1 – a2).arrow_forwardThe deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the player shots the ball in the other, then it is a goal. If the goalie jumps left and the player shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the player shots right, it is goal with probability 2/3. If both players play Nash strategies, what is the expected value of goals that will follow from this penalty shot. 1/9 2/9 3/9 4/9 5/9 6/9 O7/9arrow_forward
- Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)arrow_forwardDoes the game have a nash equilibrum and why/whynotarrow_forwardConsider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they existarrow_forward
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