Fast acquisition of cooperation and trust: A two-stage view of trusting behavior

Trustful behavior was defined in terms of the consecutive numbers of matching-to-sample problems worth money that each subject worked during sessions that ended in an equitable distribution. Two stages of acquisition are inherent in this definition; the first stage requires acquisition of an equitable method of distributing reinforcers (cooperation) to show that the within-session deviations (trust) from equity that develop during the second stage are temporary and are not part of an inequitable method of distributing reinforcers. Previous research has indicated that a contingency to trust is necessary to override the aversiveness of the inequity inherent in trusting and to produce consistent and maximal trust (half of the problems worked consecutively by each subject). The present experiment examined such a contingency. The trust contingency was an increased requirement for changing the direction of problem allocation. Only the subject who had been allocated a problem could change that allocation, by pulling a lever 45 or more times. On the other hand, no separate responses were required to allow the person who worked the last problem to also work the next one (passive trust). Hence, giving a problem was the only way to increase the distribution of problems to the other person and hence prevent oneself from receiving all of the reinforcers. All eight pairs of subjects cooperated from the outset. Trusting behavior developed for all four pairs exposed to the contingency to trust and expanded to maximal levels by the second session for three of the four pairs.     

Sample-specific ratio effects in matching to sample

In a symbolic matching-to-sample task, pigeons were trained using sample-specific, fixed-ratio “observing responses.” Subsequently, in a mixed condition, each sample was presented equally often with each ratio requirement, i.e., the ratios were no longer correlated with the samples. In a second experiment, pigeons were trained initially in the mixed condition and subsequently shifted to the sample-specific condition in which the required ratios were correlated with the samples. Results of both experiments suggested joint control of choices by ratio value and by the exteroceptive stimuli. The discriminative properties of the ratios appeared to outweigh absolute ratio-size effects.     

Choice: Some quantitative relations

Six pigeons responded in fifty-six conditions on a concurrent-chains procedure. Conditions included several with equal initial links and unequal terminal links, several with unequal initial links and equal terminal links, and several with both unequal initial and terminal links. Although the delay-reduction hypothesis accounted well for choice when the initial links were equal (mean deviation of .04), it fit the data poorly when the initial links were unequal (mean deviation of .18). A modification of the delay-reduction hypothesis, replacing the rates of reinforcement with the square roots of these rates, fit the data better than either the unmodified delay-reduction equation or Killeen's (1982) model. The modified delay-reduction equation was also consistent with data from prior studies using concurrent chains. The absolute rates of responding in each terminal link were well described by the same hyperbola (Herrnstein, 1970) that describes response rates on simple interval schedules.     

Choice between response units: The rate constancy model

In a conjoint schedule, reinforcement is available simultaneously on two or more schedules for the same response. The present experiments provided food for key pecking on both a random-interval and a differential-reinforcement-of-low-rate (DRL) schedule. Experiment 1 involved ordinary DRL schedules; Experiment 2 added an external stimulus to indicate when the required interresponse time had elapsed. In both experiments, the potential reinforcer frequency from each component was varied by means of a second-order fixed-ratio schedule, and the DRL time parameter was changed as well. Response rates were described by a model stating that time allocation to each component matches the relative frequency of reinforcement for that component. When spending time in a given component, the subject is assumed to respond at the rate characteristic of baseline performance. This model appeared preferable to the absolute-rate version of the matching law. The model was shown to be applicable to multiple-response concurrent schedules as well as to conjoint schedules, and it described some of the necessary conditions for response matching, undermatching, and bias. In addition, the pigeons did not optimize reinforcer frequency.     

Matching and maximizing with concurrent ratio-interval schedules.

Animals exposed to standard concurrent variable-ratio variable-interval schedules could maximize overall reinforcement rate if, in responding, they showed a strong response bias toward the variable-ratio schedule. Tests with the standard schedules have failed to find such a bias and have been widely cited as evidence against maximization as an explanation of animal choice behavior. However, those experiments were confounded in that the value of leisure (behavior other than the instrumental response) partially offsets the value of reinforcement. The present experiment provides another such test using a concurrent procedure in which the confounding effects of leisure were mostly eliminated while the critical aspects of the concurrent variable-ratio variable-interval contingency were maintained: Responding in one component advanced only its ratio schedule while responding in the other component advanced both ratio schedules. The bias toward the latter component predicted by maximization theory was found.     

Reinforcement and punishment effects in concurrent schedules: A test of two models

The joint effects of punishment and reinforcement on the pigeon's key-peck response were examined in three choice experiments conducted to compare predictions of Farley and Fantino's (1978) subtractive model with those made by Deluty's (1976) and Deluty and Church's (1978) model of punishment. In Experiment 1, the addition of equal punishment schedules to both alternatives of a concurrent reinforcement schedule enhanced the preference exhibited for the more frequent reinforcement alternative. Experiment 2 demonstrated decreases in the absolute response rate for each member of a concurrent reinforcement schedule when increasing frequencies of punishment were added to each alternative. Experiment 3 found that preference for the denser of two reinforcement schedules diminished when the absolute frequencies of reinforcement were increased by a constant factor and conditions of punishment for both alternatives were held constant. Diminished preferences were obtained regardless of whether the frequency of punishment associated with the denser reinforcement schedule was greater or less than that associated with the lean reinforcement alternative. The results from all three experiments uniquely supported Farley and Fantino's (1978) subtractive model of punishment and reinforcement.     

An analytic comparison of Herrnstein's equations and a multivariate rate equation

Herrnstein's equations are approximations of the multivariate rate equation at ordinary rates of reinforcement and responding. The rate equation is the result of a linear system analysis of variable-interval performance. Rate equation matching is more comprehensive than ordinary matching because it predicts and specifies the nature of concurrent bias, and predicts a tendency toward undermatching, which is sometimes observed in concurrent situations. The rate equation contradicts one feature of Herrnstein's hyperbola, viz., the theoretically required constancy of k. According to the rate equation, Herrnstein's k should vary directly with parameters of reinforcement such as amount or immediacy. Because of this prediction, the rate equation asserts that the conceptual framework of matching does not apply to single alternative responding. The issue of the constancy of k provides empirical grounds for distinguishing between Herrnstein's account and a linear system analysis of single alternative variable-interval responding.     

Choice between rewards differing in amount and delay: Toward a choice model of self control

A concurrent-chain procedure was used to study pigeons' choices between rewards differing in both amount and delay. The shorter delay terminated with a 2-second access to grain whereas the longer delay terminated with a 6-second access to grain. The ratio of the delays was constant within a given condition while their absolute values were varied. Over conditions, ratios of 6:1, 3:1, and 3:2 were studied. As the absolute values of the delays to reinforcement increased, preference for the longer-delayed but larger reward decreased under both the 6:1 and 3:1 ratios, but increased under the 3:2 ratio. These results are inconsistent with choice models predicting no change in preference when the ratios of delays and amounts are held constant. In addition, the change in preference under the 3:1 ratio is inconsistent with a simple multiplicative interaction of the trade off between reinforcer amount and delay, and suggests that delay is a more potent determinant of choice than is amount. These results have implications for models that view choice between small immediate rewards and large but delayed rewards as underlying the behavior commonly called self control.     

Toward a quantitative theory of punishment

In two experiments, pigeons' key pecking for food on concurrent variable-interval schedules was punished with electric shock according to concurrent variable-interval punishment schedules. With unequal frequencies of food but equal rates of punishment associated with the two keys and at several intensities of shock, the response and time allocation of all six pigeons overmatched the obtained relative frequency of food. The overmatching was predicted by a subtractive model of the interaction between punishment and positive reinforcement but not by two alternative models. Increases in the k and r_e parameters of the generalized matching law could not account for the observed shifts in preference.