Delay of Reinforcers in a Concurrent‐chain Schedule: An Extension of the Hyperbolic‐decay Model

Abstract

Six pigeons were trained in concurrent-chain schedules with equal aperiodic initial links and delays to reinforcers in the terminal links. The terminal links always lasted 30s. In Experiment 1, two reinforcers were delivered in each terminal link, with the first reinforcer delivered either 1 s (Experiment 1A) or 5 s (Experiment 1B) after choice. In these experiments, the delay between the first and second reinforcers in one terminal link was 10 s, and the delay between the first and second reinforcers on the other key was varied. This variation produced little change in preference. In Experiment 1C, the first and second delays on one key were lOs, and on the other key they were varied within the restriction that the sum of delays was 20s. Preference for the varied terminal link increased as the first delay was decreased. A hyperbolic model of the value of reinforcer delay provided a good description of the data from Experiment 1. In Experiment 2, a single reinforcer was delivered in each terminal link after a delay of either 0.2 or 19.8s, and these delays were reversed between conditions. The initial-link schedule providing terminal-link access was varied from means of 5 s to 480 s. As the initial-link duration was increased, preference for the shorter delay became less extreme. An extension of the hyperbolic-decay model, in which the decay constant was a hyperbolic function of the initiallink duration, described the results well. Differences between the procedure used here (constantduration terminal links) and that used in conventional concurrent-chain research precludes use of the model as a general account of concurrent-chain performance.

A Contextual Model of Concurrent‐chains Choice

“…This is a matter of notation for concurrent schedules, because the average interval between reinforcers is the reciprocal of rate. For concurrent chains, terminal-link delay and rate of reinforcement can be manipulated separately, and delay seems to be the more potent controlling variable (Davison, 1988;Davison & Smith, 1986;Mazur, Snyderman, & Coe, 1985). reinforcement value, the most general form of the matching law becomes (Baum, 1974b):…”

“…Empirical Evaluation of CCM To assess the adequacy of CCM as a quantitative model of concurrent chains, Equation 5 was fitted to every archival concurrent-chains data set meeting the following criteria: (a) at least four data points available per subject; (b) use of time-based terminal-link schedules whose delay distributions differed by a scalar multiple (i.e., FI Fl or VI VI); (c) equal terminal-link reinforcer magnitudes; and (d) obtained preference measures with a range of at least 12.5%. The data sets included independent and nonindependent (Stubbs & Pliskoff, 1969) initial links, changeover (and no changeover) delays in the initial links, response-dependent and response-independent terminallink schedules, Fl versus Fl and VI versus VI terminal links, uncued delays in blackout terminal links (Chung & Herrnstein, 1967;Davison, 1983;Gentry & Marr, 1980), and constant duration terminal links (Davison, 1988;Omino & Ito, 1993). Tandem schedules were not included (Leung & Winton, 1985;Schneider, 1972), and neither were probabilistically reinforced terminal links (Spetch & Dunn, 1987).…”

“…With this procedure, estimated values of k were used for 9 of the 92 data sets: two in Gentry and Marr (1980), five in Davison (1983), and one each in Chung and Herrnstein (1967) and Davison (1988). For these data sets, the estimate of k was always less than one, and in two cases a value of zero was obtained, indicating no effect of context.…”

Choice, delay, probability, and conditioned reinforcement

“…As explained earlier, the model was developed to predict choice in procedures with very brief choice periods. Although there has been at least one attempt to apply the hyperbolic-decay model to concurrentchain procedures (Davison, 1988), this extension was suitable for only a limited range of situations.…”

Delay and Number of Food Reinforcers: Effects on Choice and Latencies

“…When procedures have been conceptualized this way, pigeons' choices have been found consistently to favor the situation correlated with the higher sum of the immediacies even when such choices result in a lower rate of food than would otherwise be possible (Davison, 1988;Kendall, 1986;Mazur, 1984Mazur, , 1986Mazur & Vaughan, 1987;Shull & Spear, 1987;Shull, Spear, & Bryson, 1981;Snyderman, 1983). Thus, the property of the temporal distribution of reinforcers described by the sum of the immediacies metric seems to control responding quite generally.…”