Three pigeons responded for food reinforcement on multiple variable-interval schedules in which the total consumption of food was entirely determined by the subjects' interaction with the schedules (a closed economy). The finding of overmatching, where response allocation between components is more extreme than the distribution of reinforcers, was reconfirmed. Generalized-matching sensitivity decreased from overmatching to undermatching values typical of conventional multiple schedules when food deprivation was increased by decreasing session duration, but not when deprivation was increased by decreasing overall reinforcer rate. Sensitivity also increased from undermatching to overmatching as session duration increased from 100 min to 24 hr, while deprivation was held constant by decreasing overall reinforcer rate. These results can be understood in terms of increases in the value of extraneous reinforcers relative to food reinforcers as deprivation decreases or as the economy for extraneous reinforcers becomes more closed. However, no published quantitative expression of the effects of extraneous reinforcers is entirely consistent with the results.