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- 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 strategies8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…Hello, In a) I get qi=2, price=3 and profiti= 4. I had a question on (b), I attached my answer in handwritten, is it correct to do it by showing Lemma 1 result? It is so confusing. So, based on this with q(bar) as capacity constrained, and they are not gigantic capacity, I assumed it is played under pure strategy equilibrium of pricing game. Hence, the "optimal price = market-clearing" price is a Nash Equilibria as in Lemma 1. Pls, can you help me with (b)? Thanks
- Game Theory a) Consider the following game represented by the game tree below. If you observe Blue Bank playing medium and Green Bank playing bottom, would you be surprised by their choices? Carefully explain why or why not. b) Now assume that Blue and Green Banks play the game with the same actions and payoffs as in a) but they make their choices simultaneously. What is the payoff matrix for this new game? What do you predict will happen in the game? Explain. c) Assume that the game from part a) is played five times, i.e. Blue and Green Banks play a repeated game with the stage game described in a). What do you predict will happen in the game? Explain.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.The extensive form of a game is drawn when O a) the players move sequentially. Ob) the players move simultaneously. O c) there is no Nash equilibrium. O d) there are multiple Nash equilibria. O e) the game is often repeated.
- ** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.The first player can choose either U or D. If he chooses U, the second player has a choice of two strategies: L and R. If the second player moves L he obtains 1 and the first player gets 5. If the second player chooses R he obtains 2 units of payoff while the first player receives 1. Following a move D by the first player, both players engage in a simultaneous-move “Bach or Stravinsky” game (as it was described in class). Find the SPE of this game and write it down in a mixed and behavior form.Case studyIn a series of negotiations in late 1998, the UK company GEC Marconi sold its defence interests for US$12 billion â some US$3 billion more than they had been valued several months earlier. This case explains how the company used strategy dynamics and game theory to help improve the outcome.Background â worldwide consolidation in defence industriesWith the end of the Cold War in the early 1990s, many world governments were keen to reduce their defence spending. Moreover, the cost of developing new defence weapons was continuing to rise. The result of falling sales and rising costs was pressure on the worldâs leading defence companies to merge and share the costs of development and production. The first merger moves came in the USA, with a shake-out in the mid-1990s that produced three big players: Lockheed Martin, Boeing and Raytheon. Table 5.5 shows the contracts that the leading companies had with the US government in 1997.…
- 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).Consider the two-round bargaining game. The minimum the seller will sell his home for 188,000 and the maximum the buyer is willing to pay is $200,000. Both players know these two amounts and are bargaining over the difference (M=$1200). Assume the disagreement values are zero for both players. Player 1 moves first by making a proposal and Player 2 can accept and reject. If player 2 rejects Player’s 1 proposal, then Player 2 gets to make a proposal, which Player 1 can reject and accept. The game is then over. Suppose the both players discount the future income at the rate d=0.2 per period. That is, $0.20 now is equivalent to $1,00 received next round. Find the equilibrium for this 2-round game. a) Draw the game tree b) What is the sale price of home? c)Which player gets the larger share of M?Subject: Manegerial economics & policy c) Which effect dominates, the price effect or the quality effect of a price change if demand isupward sloping? d) Why might demand be downward sloping in a market with imperfect information eventhough the market is otherwise perfectly competitive? e) Why are focal points important for noncooperative games?