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We consider the problem of “fair” scheduling the resources to one of the many mobile stations by a centrally controlled base station (BS). The BS is the only entity taking decisions in this framework based on truthful information from the mobiles on their radio channel. We study the well-known family of parametric α-fair scheduling problems from a game-theoretic perspective in which some of the mobiles may be noncooperative. We first show that if the BS is unaware of the noncooperative behavior from the mobiles, the noncooperative mobiles become successful in snatching the resources from the other cooperative mobiles, resulting in unfair allocations. If the BS is aware of the noncooperative mobiles, a new game arises with BS as an additional player. It can then do better by neglecting the signals from the noncooperative mobiles. The BS, however, becomes successful in eliciting the truthful signals from the mobiles only when it uses additional information (signal statistics). This new policy along with the truthful signals from mobiles forms a Nash equilibrium (NE) that we call a Truth Revealing Equilibrium. Finally, we propose new iterative algorithms to implement fair scheduling policies that robustify the otherwise nonrobust (in presence of noncooperation) α-fair scheduling algorithms.