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- You and your friend will divide $4. You have agreed to use the following procedure.Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will chooseyour numbers simultaneously. If the sum of the amounts is less than or equal to $4, theneach of you receives the amount you named and the rest of the money is thrown away.If the sum of the amounts is greater than $4 and the amounts named are different, thenthe person who named the smaller amount receives that amount and the other personreceives the remaining money. If the sum of the amounts is greater than $4 and theamounts named are the same, then each receives $2. (a)Draw the payoff matrix of this game. Let “you” be the row player and “yourfriend” be the column player.(b) Derive the best reply functions of all players.(c) Find the Nash equilibrium (or all of the equilibria) of this game using thebest reply functions you found in part (a).Based on your answer in a, What privacy setting does the smartphone producer implement? Does the social media frim produce the app? If the smartphone producer and social media firm merged to form a single firm, qould this change the outcome you prodecited above? If so, how and not why not?Suppose that there are two firms in a market, firm 1 and firm 2. The marketis declining in size. The game starts in period 0, and the firms can compete in periods 0, 1,2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equalto 105 −10t, and they are 10.5 −t for firm 2. Monopoly profits (those if a firm is the onlyone left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of eachperiod, each firm must decide either to “stay in” or “exit” if it is still active (they do sosimultaneously if both are still active). Once a firm exits, it is out of the market forever andearns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits.What is this game’s subgame perfect Nash equilibrium?
- Consider any market that has a demand curve given by: Qd = 125 - 0.4P. Being the total quantity demanded in the market, given the quantity in millions of units and the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market that have Cmg = CVme = 2. About this market, the question is: a) What is the reaction curvature of the oligopolists? b) What will be the production of each of the companies? c) What is the sale price for oligopolists?Question 1.Assume there are only two art auction companies who account for 100% of all the sales of 19thCentury impressionist master work paintings in the world. Assume that each company buys thiskind of painting and then resells the paintings at monthly auctions. Ignoring the question of anylaws that might apply, describe what economic arrangement would maximize the twocompanies’ total profits? Show with supply and demand curves what profit they would makefrom this arrangement and what societal welfare loss, if any, results from it.a) What is the pure strategy Nash equilibrium outcome if there is one? (solved)b) Is this a socially optimal outcome? If not, which outcome is preferred? (solved)c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? (solved) d) Draw the game as a game tree (extensive form). (to be solved)e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one? (to be solved)
- Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.1.4. Suppose you are against one of two alternatives but 90% of theelectorate disagrees with your position and favors that option. Is there avoting method that is anonymous, neutral, and monotone that preventsthat option from being selected as the winning alternative?Suppose three Cournot competitors, each with costs Ci = 30qi, face an inverse market demand curve of P = 480 – 4Q. Suppose merging will not change costs. a. Find profits for the three firms. Note: Don’t round your answers. How will the profits change for F1 and for F2|3 if F2 and F3 merge? b. Suppose that after the merger occurs, F1 and the new firm F2|3 successfully collude at setting the monopoly price and output, and splitting the resulting monopoly profits. How, if at all, does this change the impact of the merger on F1 and on the merged firm?
- A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.Poker players are known to bluff once in a while, meaning that they will make a large bet despite holding inferior cards in an effort to pressure other players to fold their hands. Would bluffing be considered a dominant strategy in poker? a) No, because if a player bluffs on every hand, other players will catch on and call his or her bluff. b) No, because bluffing is usually not successful and is therefore considered a secondary strategy. c) Yes, because it usually results in a winning hand. d) Yes, because it is the main strategy used by players.[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…