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Air traffic flow control during adverse weather conditions is managed by the Federal Aviation Administration in today's air traffic system, although it is the individual airlines that are in the best position to assess the costs of disruptions to scheduled operations. To improve the efficiency of resource allocation, a market mechanism is proposed that enables airlines to participate directly in the flow control decision-making process. Since airlines can be expected to behave strategically, a lump-sum market mechanism is used for which existence of a Nash equilibrium and a bound on the worst case efficiency loss have been shown for agents that anticipate the effects of their own bids on resource prices. The convergence properties of this mechanism are studied for a two-player game with linear utilities, which reveals that restricting the airline bid update step-size can result in a wider range of stable bidding processes. The mechanism is then applied to an air traffic flow control scenario for multiple airports in the northeastern United States, which demonstrates the feasibility of performing market-based resource allocation within the time horizon for reliable weather predictions.