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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. 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.
Transcribed Image Text:4. 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.
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