1. Consider the following normal form game between A and B. Use iterated elimination of dominated strategies, if possible, to find the solution to the three games. B C1 C2 C3 1, Y 7,7 3, 10 A R1 5, 4 R2 Х, 12 9, 10 a. Let X = 5 & Y = 2. Find the solution. b. Let X = 6 & Y = 9. Find the solution. c. Let X = 3 & Y = 11. Find the solution.
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- In tic-tac-toe, assume that a player scores 1, −1, 0 respectively for a win, loss or draw. Forthe three non-isomorphic first moves in tic-tac-toe, what is the first player’s minimax valuefor each move?Mr. A,B,C, & D own company XYZ. Mr. A owns 40% of the stocks, Mr. B 20%, Mr. C 30%, and Mr. D 10%. A company policy is to be approved if at least 70% of the votes cast by the owners is attained.Note: The vote is equal to the share of stocks.1. Draw the truth table.2. Determine the canonical form in terms of product of maxterms.3. Determine the canonical form in terms of sum of minterms and minimize the expression.Consider the following linear programming model: Max 2X1 + 3X2 Subject to: X1 ≤ 2 X2 ≤ 3 X1 ≤ 1 X1, X2 ≥ 0 This linear programming model has: a. alternate optimal solutions b. infeasible solution c. redundant constraint d. unbounded solution
- A ski rental agency has n pairs of skis, where the height of the the ith pair of skis is si . There are n skiers who wish to rent skis, where the height of the ith skier is hi. Ideally, each skier should obtain a pair of skis whose height matches her/his own height as closely as possible. We would like to assign skis to skiers so that the sum of the absolute differences of the heights of each skier and her/his skis is minimized. Design a greedy algorithm for the problem. Prove the correctness of your algorithm. (Hint: Start with two skis and two skiers. How would you match them? Continue to three skis and three skiers, and identify a strategy.)In this question you will explore the Traveling Salesperson Problem (TSP). (a) In every instance (i.e., example) of the TSP, we are given n cities, where each pair of cities is connected by a weighted edge that measures the cost of traveling between those two cities. Our goal is to find the optimal TSP tour, minimizing the total cost of a Hamiltonian cycle in G. Although it is NP-complete to solve the TSP, we found a simple 2-approximation by first generating a minimum-weight spanning tree of G and using this output to determine our TSP tour. Prove that our output is guaranteed to be a 2-approximation, provided the Triangle Inequality holds. In other words, if OP T is the total cost of the optimal solution, and AP P is the total cost of our approximate solution, clearly explain why AP P ≤ 2 × OP T.Solve the problems below using the pigeonhole principle: A) How many cards must be drawn from a standard 52-card deck to guarantee 2 cardsof the same suit? Note that there are 4 suits. B) Prove that if four numbers are chosen from the set {1, 2, 3, 4, 5, 6}, at least onepair must add up to 7.Hint: Find all pairs of numbers from the set that add to 7.C) Prove that for any 10 given distinct positive integers that are less than 100, thereexist two different non-empty subsets of these 10 numbers, whose members have the samesum.An example of the 10 given numbers could be 23, 26, 47, 56, 14, 99, 94, 78, 83, 69. Onesubset of the 10 numbers could be {23, 26, 47, 56}, and another subset could be {83, 69}.The sum of the elements in the first set is 152, and it is equal to the sum of the elements inthe second subset.Hint: identify how many pigeons and how many holes you have before using the pigeonholeprinciple.
- At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…Please anwer with proper explanation and step by step solution. i will give upvote. Which of the following pairs is the best solution choice of the LP problem: Min u1 + 2u2 subject to 3u1 + u2 ≥ 7 u1 + 4u2 ≥ 6 u1, u2 ≥ 0 1. (u1, u2) = (1, 1) 2. (u1, u2) = (6, 0) 3. (u1, u2) = (1, 4) 4. (u1, u2) = (0, 7) 5. (u1, u2) = (2, 1)Let X = { ⟨Y⟩ | Y is a DFA and for every s in L(Y), ? = ab where a = b}. Show that X is decidable.
- Solution thatComputer Science Consider the demand and supply system p = ad +bdqd +ud p = as +bsqs +us with the equilibrium condition qd = qs = q. The parameters bd and bs are −2 and 1.5, respectively. Find the parameters ad and as are such that q = 5 and p = 10. Throughout this question use N = 100, and set the random seed to 14022022. The variable ud has a standard deviation of 3. All randomly generated variables have a mean of zero and are normally distributed unless something else is specified. All Monte Carlo studies should be done with 10,000 repetitions. Part a. Illustrate the supply and demand curves in a graph, together with a sample of simulated price and quantity data. Provide an additional graph where you have included the OLS estimated line of demand equation above. Are your estimates close to the true values of ad and bd ? Solve the question in Python language on Jupyter notebook.The game ping has two rounds. Player A goes first. Let mA 1 denote his first move. Player B goes next. Let mB 1 denote his move. Then player A goes mA 2 , and player B goes mB 2 . The relation AWins(mA 1 , mB 1 , mA 2 , mB 2 ) is true iff player A wins with these moves. 1. Use universal and existential quantifiers to express the fact that player A has a strategy with which he wins no matter what player B does. Use mA 1 , mB 1 , mA 2 , mB 2 as variables. 2. What steps are required in the prover–adversary technique to prove this statement? 3. What is the negation of the above statement in standard form? 4. What steps are required in the prover–adversary technique to prove this negated statement?