Consider the following normal form of the game with two players. Which of the following is the maximin strategy for the column player? O Action B O Action A X Y O There is no maximin strategy for the column player. O Action C A (4,1) (3,-1) B (-1,0) (-2,4) с (2, 1) (0, 2) 5
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- A two-person zero-sum game is given by the matrix A := −2 −3 2 −1, 2 1 −5 2, 0 −4 4 −3, 1 −2 3 0 . Find a pair of optimal strategies for this game as well as the value of the game.So I have the following roshambo strategy function to return a random play, and tests for when one of the length of plays is less than 3 and otherwise. I have tried running it many times on a single scenario to estimate the probability for each return but the results are somehow confusing. Question: Write a series for the roshambo function below to test that it works as expected. (this could be testthat::expect_equal or testthat::expect_true or testthat::expect_error tests). Thank you. roshambo <- function(plays){ # return random play if (length(plays) < 3){ return(sample(c("R", "P", "S"), 1)) } # else find most common most_common <- names(which.max(table(plays))) if (most_common == "S"){ return("R") } else if (most_common == "R"){ return("P") } else { return("S") }}Write a python code of this problem Problem Statement Assume that there are two teams and they are team attacker and team defender. Therefore, at a state of the game one agent in each team is left alive respectively. Here, the defender is given a lifeline called HP which will be assigned randomly. Furthermore, the attacker agent will try to give maximum negative HP to the defender agent to decrease his(d) chances of survival in the game. On the other hand, the defender agent will try to protect himself by receiving the lowest negative HP possible from the attacker agent. Furthermore, the attacker can have a choice from a number of bullets from his gun and the optimal moves will cost a certain maximum negative HP (chosen from randomly assigned values within the range of minimum and maximum negative HP). Here, are the following things you need to do using Alpha-Beta Pruning algorithm: Sample Input 1: Enter your student id: 17301106 Minimum and Maximum value for the…
- The Josephus problem is the following game: N people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After M passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. Thus, if M = 0 and N = 5, players are eliminated in order, and player 5 wins. If M = 1 and N = 5, the order of elimination is 2, 4, 1, 5. Write a C program to solve the Josephus problem for general values of M and N. Try to make your program as efficient as possible. Make sure you dispose of cells. What is the running time of your program? If M = 1, what is the running time of your program? How is the actual speed affected by the delete routine for large values of N (N > 100,000)? ps. provide a screenshot of output, thankssConsider the challenge of determining whether a witness questioned by a law enforcement agency is telling the truth. An innovative questioning system pegs two individuals against each other. A reliable witness can determine whether the other individual is telling the truth. However, an unreliable witness's testimony is questionable. Given all the possible outcomes from the given scenarios, we obtain the table below. This pairwise approach could then be applied to a larger pool of witnesses. Answer the following: 1) If at least half of the K witnesses are reliable, the number of pairwise tests needed is Θ(n). Show the recurrence relation that models the problem. Provide a solution using your favorite programming language, that solves the recurrence, using initial values entered by the user.Which of the following linear programming model has bounded feasible region? Group of answer choices A. max ?=3?+2?subject to the following:??+4???≥4−?≥10≥0≥0max z=3x+2ysubject to the following:x≥4−yx+4y≥10x≥0y≥0 B. max ?=3?+2?subject to the following:?+????≤4≤10−4?≥0≥0max z=3x+2ysubject to the following:x+y≤4x≤10−4yx≥0y≥0 C. None of the above D. max ?=3?+2?subject to the following:??+2???≥10−?≥2≥0≥0
- Please solve the following problem. Quiz = Pass Quiz = Fail AI = Fail 0.1 0.2 AI = Pass 0.6 0.1 Mid = Pass Mid = Fail AI = Fail 0.2 0.2 AI = Pass 0.5 0.1 Suppose you have three events AI Grade, Quiz, and Mid. Here each event has two possible outcomes, either pass or fail. Additionally, given that AI Grade is observed, Quiz and Mid become independent of each other. Also, out of every 100 students, 30 students fail the AI course. Now, using the joint probability tables given, calculate P(AI Grade=Pass, Quiz=Fail, Mid=Fail).Given the following linear programming model; Who are the basic variables on the initial board? MAX Z = 5 X1 + 5 X2 Hold it: 12 X1 + 8X2 <= 96 6 X1 + 12X2 <= 72 X1 <= 2 X1, X2> = 0 Select one: a.All b.h1; h2 c.X1; X2 d.None e.h1; h2; h3: You have a basketball hoop and someone says that you can play one of two games.Game 1: You get one shot to make the hoop.Game 2: You get three shots and you have to make two of three shots.If p is the probability of making a particular shot, for which values of p should you pick one gameor the other?