Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game. 2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.

Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game. 2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

See similar textbooks

Related questions

Q: Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n; 20-n);…

A: GIVEN Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n;…

Q: Exercise 2. Consider the mixed extension of the 2-person game defined by the payoff- matrices ^ - (…

A: Game theory includes Nash equilibrium. It means that if there are two players in the economy and…

Q: Try to solve the following extensive-form game by backward induction, then covert them into…

A: Suppose, that P2 is already in the market whereas P1 is planning to enter. P2 has two alternative…

Q: Problem 6. Does there exist a two-player game that has a pure NE but best response dynamics may not…

A: According to Game Theory, the Best response is the strategy(or strategies) that gives the most…

Q: Following question 11, what is the Nash equilibrium of this game under a rule of no liability? a) I…

A: Nash equilibrium is a part of game theory, it is a equilibrium at which none of the parties involved…

Q: Which of the following statements is true? For every normal-form game Iy = [I; {S.}; {u,()}}, if the…

A: The dominant strategy is the strategy in which different individuals do not know the strategy of…

Q: Q. 2. Consider the game of voters participation. Two candidates A (with two suporters) and B (with…

A: The ideal conclusion of a game occurs where there is no incentive to depart from the beginning…

Q: Exercise 3. Consider the following game in normal form. L U 4, 4 1, 6 D 6, 1-3, -3 (a) Find all the…

A: L R U 4,4 1,6 D 6,1 -3,-3

Q: Q. 2. Consider the game of voters participation. Two candidates A (with two suporters) and B (with…

A: please find the answer below.

Q: 1. Players 1 and 2 are bargaining over how to split 5 dollars. Player 1 proposes to take si dollars…

Q: Consider a game where two firms can choose either low or high fares. The payoffs are Firm2 Firm2…

A: Meaning of Decision Theory under Nash Equilibrium: Under decision theory, it is a systematic…

Q: Find ALL pure-atrategy Subgame Nash Equilibria (you may ignore mixed strategies). Be sure to pay…

A: We are going to find the Subgame Perfect Nash Equilibrium to answer this question.

Q: In the following symmetric general sum game (2, 2) (0,0) (0,0) (0,0) (0,0) (2, 2) (0,0) (2,2) (0, 0)…

A: Given information Pay off for 2 players

Q: (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium…

A: The matrix looks like: The payoff looks like - (Rose,Colin)

Q: Selten's Horse: Consider the three-person game described in Figure 15.6, known as Selten's horse…

A: Selten's horse is a game with incomplete information where one agent is unsure about the payoffs or…

Q: Person A English Chinese English 10,10 5,0 Person B Chinese 0,5 5,5 A) Find the Nash equilibria of…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: b. Which of the following is/are the Nash equilibria to this game? Instructions: In order to receive…

A: We will use game theory concept to answer this question.

Q: Consider the following game. Which one of the following statements is TRUE? 1. There are 8…

A: In this game, there are 7 sub-games for this extensive form game, which are For player -1, the…

Q: Consider the following game (image attached) (i) Can Backward induction be applied in this…

A: In the field of game theory, a Nash Equilibrium is a collection of strategies, one for each…

Q: P A (12, 12) B (26,70) C (11,0) (3,25) (24,26) D (5,-10) (16,-8) (13,-8) R (8,-5) (-2,6) S (25, 14)…

A: In a payoff matrix the first value refers to the payoff received by player 1 and the second value…

Q: In the following normal form game, perform iterated elimination of strictly dominated strategies.…

A: The Nash equilibrium best course of action provided the strategy of rival firm has been given.

Q: Consider the game with the payoffs below. Check ALL the Nash equilibria (if any), multiple answers…

A: Nash equilibrium is such equilibrium from where no player has any incentive to change its strategy.…

Q: Apply the method of backwards induction to compute a Nash equilibrium of the following game. (For…

A: In backward induction method we start from end nod of the payoffs and accordingly eliminate the…

Q: 6. Find the median and all pure Nash equilibria of the corresponding doctor location game for the…

A: Answer - Need to find- Median and all pure Nash equilibrium Given in the question-

Q: а.) Your Crush Love Friendship You Love (100, 60) (30, 120) Friendship (60, 50) (40, 40) i. What…

A: Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there…

Q: b) Two players, both with zero wealth, bargain over how to divide £X > 0 between them. Failure to…

A: given Two players, both with zero wealth, bargain over how to divide £X > 0 between them.…

Q: Q. 2. Consider the game of voters participation. Two candidates A (with two suporters) and B (with…

A: Game theory has a notion known as Nash equilibrium, which states that the best possible outcome is…

Q: Design the payoffff matrix of a game with no Nash Equilibria. The game should have 2 players, 2…

A: Nash Equilibrium is a solution to a non-cooperative game consisting of two or more players,…

Q: P1 R P2 3 U 8 P1 P1 R' L' R' L' 4 (a) Find subgame perfect Nash equilibria of the game above. (b)…

A: Players: {P1, P2} Actions: P1 Action = { R, L} P2 Action ={U, T} Strategies: P1 Strategy = {RR' ,…

Q: 5

A: Nash equilibrium More specifically, the Nash equilibrium is a game theory concept that states that…

Q: Player 2 1 2 1 (0,2) (1,0) (0,2) Player 1 2 (1,0) (0,2) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure.…

Q: Consider the following normal form game. A D 10, 10 Player 1 E-12,-1 F 15, -1 Player 2 B -1,-12 8,8…

A: The given payoff matrix looks like this:

Q: Show that there does not exist a pure-strategy perfect Bayesian equilibrium in the following…

A: Given diagram,

Q: Now assume the game is simplified into two strategies for each player. Paul plays T or B, and Stella…

A: d) Pure strategy equilibrium To find out the pure strategy equilibrium, we use the best responses…

Q: Three firms share a market. The demand function is P(q1, 92, 93) = 10 – q1 – 92 – 93, where q; is…

A: We have firm 1 as a leader and firm 2 and 3 as the followers.

Q: Exercise 2. Consider the mixed extension of the 2-person game defined by the payoff- matrices 5 1 A…

A: Introduction Nash equilibrium is a part of game theory. It means that if there are two players in…

Q: Problem 1. Consider the following game. Notice that player 2 has two information sets. L M a e 2,2…

A: In the backword induction we first solve for player who is moving last in the game.

Q: 2. Paul and Stella play a game with three strategies each, T, M, and B for Paul, and L, C, and R for…

Q: Player 2 4, 4 0,2 Player 1 M 2,0 2,2 B. 3,0 1,0 a) Find the the pure-strategy Nash equilibria b)…

A: Taking positive probability p1, p2 and 1-p1-p2 for T, M and B respectively. And q1 and 1-q1 for E…

Q: bria in the stan

A: Multiplicity helps in prediction of multiple possible outcomes for a given input in a model without…

Q: 4. Consider a normal form game with N= {1,2} and S= {A,B,C,D} × {W,X,Y,Z}. Assume that L1 allows to…

A: Conclusion Despite the overwhelming evidence to the contrary, some strategy researchers continue to…

Q: Are the following true or false (justify answer: just T or F will not suffice): A) In a sequential…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: P2: Hawk Dove P1: Hawk -25, -25 50, 0 Dove 0, 50 15, 15 Is the mixed-strategy NE of the above game…

A: Evolutionary stable strategy is a strategy which if adapted, then an alternative strategy cannot…

Q: Head 1, -1 -1, 1 Tail -1, 1 1, -1 Vhich of the followings are the Nash equilibria of this game? (You…

A: We will use underlining method to find the Nash equilibrium in this game.

Q: Is the set of SPE of any extensive form game with perfect information is identical to the set of…

A: An extensive-form game is a game theory specification that allows for the explicit representation of…

Q: Consider the Sequential Matching Pennies Game. Now assume player 1 is allowed to quit the game in…

A: Matching Pennies is a simple game theory scenario that demonstrates how rational decision-makers…

Q: a) Find the pure strategy Nash Equilibrium for the subgame starting at player l's second decision…

Q: a. b. Consider the following game G: A B 4, -4 7,-7 8,-8 6,-6 X Y Is there a pure Nash equilibrium…

A: When Player 1 plays X, player 2 have the following strategies to play and their corresponding…

Question

100%

1. Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game.

2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Part 1

Part 1 (Contd..)

Part 2

Part 2 (Contd..)

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
H7. Find all pure strategy Nash equilibria and for each one, state whether or not it is subgame perfect.
See the extensive form game image attached. 1) Solve the game by backward induction 2) Find all the pure-strategy Nash equilibria (in complete contingent plans)of the extensive-form game (no need to write down thenormal-form representation)
on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
1. Consider the following simultaneous move game Player 2 C D Player 1 A 4,3 4,-2 B 2,2 3,-1 C 3,0 4,0 d) Suppose the game is now played sequentially where Player 1 chooses first, player 2 observes 1’s choice and then makes his own choice. What are the Nash equilibria of this sequential game?
A) Focus on the strategic game at the lower-right side of the gametree. Find all the Nash equilibria for this subgame, including the mixed-strategyones. (b) Find all the subgame perfect equilibria for the entire game, allowingfor both pure and mixed strategies
Micro Nash game theory Show that if in a game G, the sets of actions (A i) i in N are compact, and the payment functions (u i) i in N are continuous, then for all i in N, the application of Best response has a closed graph. Conclude that the application of best response has a closed graph.
1 True or False : Every finite extensive - form game of imperfect information admits at least one pure - strategy Nash equilibrium . Justify if true or give a counter - example if not
E3 Bayesian Game]. Consider a Bayesian game described by a following payoff matrix. Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.
Consider Bernard \ Mary Left Center Right Top 0,5 1,0 2,2 Bottom 1,0 0,3 2,2 The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5. a Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain.Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC . b Give all mixed strategy Nash equilibria of this game.
1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?
There are three players who must each choose an “effort” level from 1 to 7, that is, Si = {1, 2, 3, ..., 7}. The payoff for each player i is ui(si, s−i) = 10 max{s1, s2, s3} − si. How many pure- strategy Nash equilibria are there? Select one: a.2 b.4 c.none of the other answers d.3 e.1