Rats' choices between one and two delayed reinforcers

Rats chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A left leverpress led to two reinforcers, each delivered after a fixed delay. A right leverpress led to one reinforcer after an adjusting delay. The adjusting delay was increased or decreased many times in a session, depending on the rat's choices, in order to estimate an indifference point--a delay at which the two alternatives were chosen about equally often. Both the number of reinforcers and their individual delays affected the indifference points. The overall pattern of results was well described by the hyperbolic-decay model, which states that each additional reinforcer delivered by an alternative increases preference for that alternative but that a reinforcer's effect is inversely related to its delay. Two other possible delay-discounting equations, an exponential equation and a reciprocal equation, did not produce satisfactory predictions for these data. Adding an additional free parameter to the hyperbolic equation as an exponent for delay did not appreciably improve the predictions, suggesting that raising delay to some power other than 1.0 was unnecessary. The results were qualitatively similar to those from a previous experiment with pigeons, but quantitative differences suggested that the rates of delay discounting were several times slower for rats than for pigeons.