Please help with #3- A and B Q3. Suppose the following dynamic game:(-1,0)APlayer 1Player 2(1,0)HHa. How many subgames in this game?b. Find all pure subgame perfect Nash equilibria.Player 1ΤΗ(1,-1) (-1, 1) (-1, 1) (1,-1)Q4. Consider a Cournot competition model with two firms, 1 and 2. They produce identicalgoods in the same market with demand function P = 120-5Q, with Q=q1+q2. Furthermore,their production process generates pollution to the environment, which increases their cost ofproduction. Their cost functions are given byC₁(91, 92) = 10 q₁² +592C₂(91, 92) = 1092 +591(a) Calculate their equilibrium quantities and prices for both firms.(b) Consider they collude and form a cartel, that is they perform together as a monopoly andmaximize their total profits. Calculate new equilibrium quantities and prices.

Duopolies are found in explaining the linear or sequential games. As these models show the…

Answered: Q3. Suppose the following dynamic game:…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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if w = 6 (a) This game has a unique (pure strategy) Nash equilibrium ⟨t*1 , t*2 ⟩ in which t*1 = t*2 Find the value of t*1 . (If your answer is a fraction, report it in lowest terms.) (b) To which strategy t2 is the strategy t1 = 4 a best response? (If your answer is a fraction, report it in lowest terms.)
Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
The Chinese government has created a fund worth more than 20 trillion won to foster the semiconductorindustry. Although there is a large technological difference between memory semiconductors, systemsemiconductors can be developed in a short period of time. The number of companies producinghomogeneous quality products has increased.￭Question (a) In the Cournot game, when the number of firms increases from 2 to n, compare the output,total output, and profit of each firm with N.E. in the Cournot model. ￭Question (b) If the number of companies participating in the semiconductor market increases to infinity,that is, in a perfectly competitive market, what will be the equilibrium point?
Consider a first-price sealed bid auction of a single object with two bidders j = 1,2 and no reserved price. Bidder 1's valuation is v1 = 2. and bidder 2's valuation is v2= 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts. In the event of a tie, the object is awarded by a flip of a fair coin. Is there a Nash equilibrium? What is it? Is it unique? Is it efficient?
Consider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.
When it comes to customs clearance of goods, customs officers and smugglers try to prevent the otherparty from predicting their respective intentions. Their respective profit metrics are as follows:￭There is no general Nash equilibrium (pure strategy).￭Question: What is the mixed strategy equilibrium? – find out x and y
A seller would like to sell a painting using second price (Vickrey) auction. The seller knows that there are three buyers and each buyer is equally likely to have High (H), Medium (M), or Low (L) valuation for the painting. The valuations of the buyers are independently distributed. Assuming that the buyers will play the Nash equilibrium in the second price auction, how much revenue will the seller make?
Consider the following normal form of the game with two players. What is the Nash Equilibrium of this game?
can we find nash equilibrium through mixed strategy as well?
Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y ?(Total number of times he roll the die is 4.)

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Q3. Suppose the following dynamic game: Player 1 Player 2