4. The matching game is played in a bipartite graph G = (V₁, V2, E) in which edges are connectonly vertices V₁ to vertices in V₂. The players are the vertices in the graph that is V₁ 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.

Answered: Image /qna-images/answer/62a5dc42-2af9-422e-8319-0b84d38ac392.jpg

Answered: The matching game is played in a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 80EQ

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Compute the vertex set V and edge set E of the graph G = (V,E) whose Prufer Code is (3, 3, 3,3, 3, 3). Select one: OV={1,2,...,8} and E = {(1,3), (2, 4), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} {(1,4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} %3D OV={1,2,..., 8} and E = OV= {1,2,... ,8} and E = {(1, 4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} OV= {1,2,..., 8} and E = {(1,3), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} Clear my choice
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2. In a round-robin tournament the Tigers beath the Blue Jays, the Tigers beat the Cardinals, the Tigers beat the Orioles, the Blue Jays beat the Cardinals, the Blue Jays beat the Orioles, and the Cardinals beat the Orioles. Model this outcome with a directed graph.
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I want this to be considered as a Advanced Math question pls. . Consider a graph G which is a complete bipartite graph. The graph G is defined as K(3,4), meaning it has two sets of vertices, with 3 vertices in one set and 4 in the other. Every vertex in one set is connected to every vertex in the other set, but there are no connections within a set. Calculate the number of edges in graph G. Also, determine if the graph G contains an Euler path or circuit, and justify your answer.
let n>=2 be a natural number Let V be the set of people in a party of n people. Use set-builder notation o define E in the undirected graph G=(V,E) where there is an edge between two vertices u and v if the person u and v have met each other. What does the degree of edge in G represent? Prove that there cannot be two vertices u and v in V such that deg(u)=0 and deg(v)=n-1 at the same time. Use part 2 and 3 along with pigeon hole principle to show that in every party of n people, there is always two people who both have met exactly the same number of people.
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Draw the graph K3,4, and extract a perfect matching from it.

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