3. Construct your own two-player 2 × 3 game in which none of the actions of either player is weakly dominated by another action, but one of the (three) actions of player 2 is strictly dominated by a mixed strategy. Then find all mixed strategy Nash equilibria of your game.
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- 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?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.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…
- Can you find a stable outcome for the following network, if possible. If not, please explain why.A two-person zero-sum game with an nn rewardmatrix A is a symmetric game if A AT.a Explain why a game having A AT is called asymmetric game.b Show that a symmetric game must have a value ofzero.c Show that if (x1, x2,..., xn) is an optimal strategyfor the row player, then (x1, x2,..., xn) is also an opti-mal strategy for the column player.d What examples discussed in this chapter are sym-metric games? How could the results of this problemmake it easier to solve for the value and optimal strate-gies of a symmetric game?3. Consider a training set that contains 100 positive examples and 400 negative examples. Foreach of the following candidate rules,R1: A −→ + (covers 4 positive and 1 negative examples), R2: B −→ + (covers 30 positive and 10 negative examples),R3: C −→ + (covers 100 positive and 90 negative examples),determine which is the best and worst candidate rule according to:(a) The likelihood ratio statistic.
- Consider 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.A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Suppose the buyer uses a strategy p1(b) = 1/12 + (2/3)b and the seller uses a strategy p2(s) = 1/4 + (2/3)s. Suppose the buyer's value is 3/4 and the seller's valuation is 1/4. Will there be a transaction? Explain. Is this strategy profile a Bayesian Nash equilibrium? Explain.You are required to create a Julia program that does the following in this problem:Analyze every policy you are given, then tweak it until a solution is discovered. Real-time recording and saving of the Markov decision process (MDP).