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- Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.Please solve Fast i give upvote. Do not use chatgpt.+6) i) ii) Two companies share the bulk of the market for a particular kind of product. Each is now planning its new marketing plans for the next year in an attempt to wrest some sales away from the other company. (The total sales for the product are relatively fixed, so one company can increase its sales only by winning them away from the other.) Each company is considering three possibilities: (1) better packaging of the product, (2) increased advertising, and (3) a slight reduction in price. The costs of the three alternatives are quite comparable and sufficiently large that each company will select just one. The estimated effect of each combination of alternatives on the increased percentage of the sales for company 1 is as follows: Each company must make its selection before learning the decision of the other company. Strategy 1 Player 1 2 3 1 2 1 3 Player 2 2 3 4 -2 3 1 0 Without eliminating dominated strategies, use the minimax (or maximin) criterion to determine the best…
- b) Consider the following game matrix: 1 3 -1 4 2 6 1 2 0 A = -3 5 i) Determine the optimal strategies to both players using the Graphical method. ii) Determine and interpret the value of the game.4 In a gambling game, Player A and Player B both have a $5 and a $10 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. (a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Player B Player A $5 $10 $5 (b) Is there a pure strategy? Why or why not? ---Select--- . Since the maximum of the row minimums is --Select--- (c) Determine the optimal strategies and the value of this game. probability Player A selects $5 probability Player A selects $10 probability Player B selects $5 probability Player B selects $10 = = $10 = = Does the game favor one player over the other? Yes O No and the minimum of the column maximums is (d) Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the…5.q1
- Problem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)(a) Assuming that each fishery chooses fi ∈ (0, F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? 4 (c) Suppose that a benevolent social planner wants maximize the utility of both fisheries. In other words, the social planner solves the following problem: max w(f1,f2) w(f1, f2) = u1(f1, f2) + u2(f1, f2) =2 ln(f1) + 2 ln(f2) + 2 ln(F − f1 − f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?!
- Two coins are tossed : (a) if A, is the event that the first coin is a tail and A, is the event that the second coin is a tail and A, is the event that the second coin is a head are A, and A, mutually exclusive ? Obtain P(A, U A) and P(A, n A,), (b) if further the event A, is that both the coins are heads and A, is that both the coins are tails are A, and A, mutually exclusive ? Are they exhaustive ? Obtain P(A, UA,).2a) 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)