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We introduce a new model of congestion games that captures several extensions of the classical congestion game introduced by Rosenthal in 1973. The idea here is to parameterize both the perceived cost of each player and the social cost function of the system designer. Intuitively, each player perceives the load induced by the other players by an extent of ρ ≥ 0, while the system designer estimates that each player perceives the load of all others by an extent of σ ≥ 0. For specific choices of ρdoi:10.1016/j.tcs.2018.04.025 fatcat:7zogde56hngdxm633m5apy4nya