The matching game is played in a bipartite graph G = (V₁, V2, E) in which edges are connect only 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 is mutual (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 of the matching game. Analyze the complexity of the problems related to pure Nash equilibria for this family of games.

The matching game is played in a bipartite graph G = (V₁, V2, E) in which edges are connect only 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 is mutual (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 of the matching game. Analyze the complexity of the problems related to pure Nash equilibria for this family of games.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.5: The Format Proof Of A Theorem

Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...

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