4. The matching game is played in a bipartite graph G = (V1, V2, E) in which edges are connectonly vertices Vị to vertices in V2. The players are the vertices in the graph that is Vi U V2.Each player has to select one of its neighbors. Player i gets utility 1 when the selection ismutual (player i selects j and player j selects i) otherwise he gets 0.Provide a formal characterization of the strategy profiles that are pure Nash equilibrium ofthe matching game. Analyze the complexity of the problems related to pure Nash equilibriafor this family of games.

Algorithm: function matching_game(G, u) foreachplayer i in G.V foreachplayer j in G.V if i != j…

Answered: The matching game is played in a…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Consider the doctor-patient problem. There is a Doctor's clinic which has one Doctor, one patient chair, and n chairs for waiting for patients if there are any to sit on the chair. If there is no patient, then the Doctor sleeps in his own chair. When a patient arrives, he has to wake up the Doctor. If there are many patients and the Doctor is treating a patient, then the remaining patients either wait if there are empty chairs in the waiting room or they leave if no chairs are empty. Write a solution (Algorithm / Pseudocode) using semaphores.
1. Consider the generalization of stable matching problem where a certain man-woman pairs are forbidden. The set of forbidden pairs is denoted as F. Each man m ranks all the woman w for which (m, w) ¢ F and each woman w ranks all the man m for which (m, w) ¢ F. Consider the following algorithm for finding a stable matching that consists of only unforbidden pairs: Initially all mE M and w e W are free; S = Ø While there is a man m who is free and hasn't proposed to every woman w for which (m, w) ¢ F Choose such a man m Let w be the highest-ranked woman in m's preference list to which m has not yet proposed If w is free: Add (m, w) to solution S Else (w is current matched with m'): If w prefers m' to m m remains free Else Replace (m', w) by (m, w) in S Return solution S Answer true or false for the following questions: (a) Any woman w remains engaged from the point at which she receives her first proposal, and the se- quence of partners to which she is engaged get better and better. (b)…
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For problem 2, you should provide two answers for each of the search strategies: the states expanded and the solution. Problem 2 Alice the agent wants to go skiing right after AI class is over. She starts in the lecture hall (the "Start" state below) and wants to make it to Alta (the "Goal" state) as soon as possible. There are several possible paths she can take denoted in the graph below ( refer to image ): The available actions at each state are denoted by arrows with a path cost label above each arrow. For each of the following graph search strategies, figure out the order in which states are expanded as well as the path returned by graph search. When choosing an arbitrary order of state expansions (to break ties), use alphabetical ordering. Remember that in graph search, states are expanded only once. Depth-first search Breadth-first search Uniform cost search A* search
Given the following input instance for the 0/1 Knapsack problem. Show how the algorithm given in the class works on this input instance. Complete the whole (M+1)x(n+1) table, and give the answer for the optimal solution, where M is the capacity of the knapsack and n is the number of objects. Object 1 Object 2 Object 3 Object 4 Object 5 Object 6 Profit p Weight w; | 2 3 3 5 5 1 4 4 5 3 2 5 М-10
Correct answer will be upvoted else Multiple Downvoted. Computer science. Players alternate, Alice moves first. Each turn a player picks any component and eliminates it from the exhibit. In the event that Alice picks even worth, she adds it to her score. On the off chance that the picked esteem is odd, Alice's score doesn't change. Essentially, on the off chance that Bob picks odd worth, he adds it to his score. On the off chance that the picked esteem is even, Bob's score doesn't change. On the off chance that there are no numbers left in the cluster, the game finishes. The player with the most noteworthy score wins. Assuming the scores of the players are equivalent, a draw is announced. For instance, assuming n=4 and a=[5,2,7,3], the game could go as follows (there are different choices): On the principal move, Alice picks 2 and get two focuses. Her score is presently 2. The exhibit an is presently [5,7,3]. On the subsequent move, Bob picks 5 and get five…
TYPEWRITTEN ONLY PLEASE FOR UPVOTE. DOWNVOTE FOR HANDWRITTEN. DO NOT ANSWER IF YOU ALREADY ANSWERED THIS. I'LL DOWNVOTE.
Consider the following directed graph. E N B C Which of the following are valid cycles? A, A, D A, D, C, A A, A, A, A, A C, E, B, C A E, D, C, B, E C, E, B
Consider the following edge-weighted graph with 10 vertices and 17 edges. V-w weight A-B 8. F-A 6. G-B 15 B-F C-B D-C 16 C-G 12 C-H C-I D-I 17 D-E 11 I-E 13 J-E 10 G-F 9. H-G I-H 14 1 I-J Here is a graphical representation of the same edge-weighted graph: (A) -8- (C)------16----- (D)---- --11-----(E) 7|\ 13 10 (F) (G) Give the sequence of edges in the MST in the order that Prim's algorithm adds them to the MST, when starting Prim's algorithm from vertex H. To specify an edge, use its weight.
Consider navigating the maze shown below. 4. 1. S 2. A 3. 5. 6. 7. L N 8. M 2 2 4 C E 2 P 2 2 A G The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let S be the initial state and G be the goal state. List the first 8 vertices expanded by Uniform Cost Search (enter the single letter label of a node). S B K FL 2 J 2 2 D H
3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. (a) One way to do this is to input the adjacency matrix A, calculate A², then output all pairs (i, j) for which A(i) > 0. Defining scalar multiplication and addition as "basic operations," up to a constant c, how many "basic operations" are required to calculate A², in terms of n and m? (Hint: First think about how many operations are required to calculate each entry of A², then multiply by the number of entries.) (b) Suppose that we want to know the number of agents who are connected by a walk of length k in a given network, where k≥ 1. Up to a constant, how many basic operations are required to calculate Ak, in terms of n and m? (c) (Harder) We showed in class (Lecture 4) that a simple adaptation of…
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