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In opinion formation games with directed graphs, a bounded price of anarchyis only known for weighted Eulerian graphs. Thus, we bound the price of anarchyfor a more general class of directed graphs with conditions intuitively meaningthat each node does not influence the others more than she is influenced, wherethe bounds depend on such difference (in a ratio). We also show that thereexists an example just slightly violating the conditions with an unboundedprice of anarchy.

Bounds on the Price of Anarchy for a More General Class of Directed Graphs in Opinion Formation Games