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- Game Theory. 1. Yuppie town has two food stores, LA Boulangerie, which sells bread, and La Fromagerie, whichsells cheese. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If LaBoulangerie's price is P 1 dollars per loaf of bread and La Fromagerie's price is P 2 dollars per pound ofcheese, their respective weekly sales, Q 1 thousand loaves of bread and Q 2 thousand pounds ofcheese, are given by the following equations: a) For each store, write its profits as a function of P 1 and P 2 , and find the Nash equilibriumprices in this game. b) Suppose that the two stores collude and set prices jointly to maximize the sum of theirprofits. Find the joint profit-maximizing prices for the stores.c) Provide an explanation for the differences between the Nash equilibrium prices and thosethat maximize joint profits.Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 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.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.
- Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…Exercise 7: The facility location game. Our example is a game in which two firms compete through their choice of locations. Suppose that two firms A and B are each planning to open a store in one of six towns located along six consecutive exits on a highway. We can represent the arrangement of these towns using a six-node graph as in Figure 1 Now, based on leasing agreements, Firm 1 has the option of opening its store in any of towns 1, 3, or 5, while Firm 2 has the option of opening its store in any of towns 2, 4, or 6. These decisions will be executed simultaneously. Once the two stores are opened, customers from the towns will go to the store that is closer to them. So for example, if Firm A open its store in town 3 and Firm B opens its store in town 2, then the store in town 2 will attract customers from 1 and 2, while the store in town 3 will attract customers from 3, 4, 5, and 6. If we assume that the towns contain an equal number of customers, and that payoffs are directly…Exercise 3: merger example Algoma Steel Inc. and Stelco Steel Inc. Merger? Suppose you work at the Bureau and your task is to assess a proposed merger between Algoma Steel Inc. and Stelco Steel Inc. For simplicity, these are the only two firms in Canada. The cost of this merger is that the two firms will become one joint firm, or the duopolists become the monopolist. This is likely to limit consumer choices and the equilibrium price is likely to rise. However, this merger is likely to increase economies of scale, or production cost will fall. From existing studies you know the following information, and P is the price per ton of steel and Q is the number of tons of steel. Demand for steel: P = 1,800 - Q Marginal revenue: MR = 1,800 - 2Q Supply of steel: MC = ATC = 600, identical across the two firms. Case #1: Before Merger - Cournot duopoly - the government does not intervene The total surplus (TS), defined as the sum of consumer surplus and producer surplus, is equal to…
- 7. High-tech Industry Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget: Synergy's Decision Large Budget Small Budget Dynaco's Decision Large Budget $30 million, $20 million $70 million, $0 Small Budget $0, $30 million $50 million, $40 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy a dominant strategy. If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco a dominant strategy. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.) True FalseGame Theory. Elaborate an example of a mixed strategy, includes explanations of the development of the solution. Please be as clear as possible.5 WHILE USING GAME THEORY METHOD EXPLAİN CLİMATE CHANGE STRATEGIES PLAYERS PAYOFFS AND OUTCOMES IN 200 WORDS
- Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)(a) What are the sets of pure strategies of players A and B?(b) Find the subgame perfect equilibrium(c) Provide a brief argument why the SPE is unique (i.e., why there are no more SPE, whether in pure or mixed strategies).QUESTION 1: Game theory a) What is the pure strategy Nash equilibrium outcome if there is one? b) Is this a socially optimal outcome? If not, which outcome is preferred? c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? d) Draw the game as a game tree (extensive form). e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one?
