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How reinforcer type affects choice in economic games
Behavioural Processes 75 (2007) 107–114
How reinforcer type affects choice in economic games Edmund Fantino ∗ , Santino Gaitan, Art Kennelly, Stephanie Stolarz-Fantino University of California, San Diego, United States Received 25 August 2006; received in revised form 8 December 2006; accepted 8 December 2006
Abstract Behavioral economists stress that experiments on judgment and decision-making using economic games should be played with real money if the results are to have generality. Behavior analysts have sometimes disputed this contention and have reported results in which hypothetical rewards and real money have produced comparable outcomes. We review studies that have compared hypothetical and real money and discuss the results of two relevant experiments. In the first, using the Sharing Game developed in our laboratory, subjects’ choices differed markedly depending on whether the rewards were real or hypothetical. In the second, using the Ultimatum and Dictator Games, we again found sharp differences between real and hypothetical rewards. However, this study also showed that time off from a tedious task could serve as a reinforcer every bit as potent as money. In addition to their empirical and theoretical contributions, these studies make the methodological point that meaningful studies may be conducted with economic games without spending money: time off from a tedious task can serve as a powerful reward. © 2007 Elsevier B.V. All rights reserved. Keywords: Altruism; Economic games; Optimality; Reinforcer type; Sharing game
1. Introduction
2. Comparing monetary and non-monetary incentives
Studies with meaningful payoffs and a sufficient number of subjects can be expensive to conduct if the payoffs are made in real money. Thus, psychologists have often used hypothetical money as the payoff in the expectation that the general pattern of results would be the same as if real money were distributed. Economists have used real money and have asserted that results with hypothetical money may not have external validity. These differing viewpoints were discussed at length in the target article and commentaries in Hertwig and Ortmann (2001). Fantino and Stolarz-Fantino (2001) cited several studies from their laboratory suggesting that comparable results are obtained with points backed or not backed by real money. Studies in which results with hypothetical and real money were comparable include those of Case and Fantino (1989) on the conditions under which information reinforces observing behavior, Goodie and Fantino (1995) on a behavioral analog of base-rate neglect, and StolarzFantino et al. (2003) on the effects of monetary reinforcement and feedback on the conjunction fallacy.
Case and Fantino (1989)’s study was one in a series of studies from our laboratory, primarily with human subjects, that explored the conditions under which adults and children would make observing responses—that is, responses the only function of which was to produce stimuli correlated with the schedule of reinforcement in effect. The results of these studies, along with those from other laboratories, notably that of Dinsmoor with pigeons as subjects (e.g., Dinsmoor, 1983; Dinsmoor et al., 1972), suggested that observing was not maintained by production of a stimulus correlated with the absence of reinforcement but only by the production of a stimulus differentially correlated with reinforcement. In other words, an informative stimulus maintained observing only when the stimulus was correlated with a richer reinforcement environment than that present in the absence of the stimulus. These results supported versions of the conditioned reinforcement account of observing but were incompatible with accounts stressing that information per se was reinforcing (for a review of both positions see Fantino, 1977). The human studies supporting the conditioned-reinforcement account of observing used points – not money – as a reinforcer (e.g., Case et al., 1985; Fantino and Case, 1983), though Fantino et al. (1983) used marbles with some of their children. Perhaps the reinforcing potency of an (informative) extinction stimulus would become evident if the students’ responding resulted in
∗ Corresponding author at: Department of Psychology, 0109, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0109, United States. Tel.: +1 858 534 3927; fax: +1 858 534 7190. E-mail address: [email protected] (E. Fantino).
0376-6357/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2007.02.001
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points backed by real money. Thus, Case and Fantino (1989) included a study in which points were not backed by money in one condition, points were each worth 5 cents in a second condition, and points were each worth 25 cents in a third condition. The results showed that the incentive had no discernible effect on rate of observing. In the critical condition, preference for the informative S- was pitted against preference for a totally uninformative stimulus. No matter what the incentive, preference for the informative S- was significantly below .50. Moreover, in none of the conditions was a systematic effect of incentive evident. Avoidance of even useful information is central to base-rate neglect, in which, when predicting an event, educated students neglect the molar frequencies of the possibilities and instead overemphasize case-specific information (e.g., Kahneman and Tversky, 1973). A classic example is adapted from Tversky and Kahneman (1982):
Our third and final example comes from a study on factors controlling the conjunction fallacy, another logical fallacy discussed by Tversky and Kahneman (1983). Our version of the fallacy (Experiment 5 in Stolarz-Fantino et al., 2003) concerned an individual named Ralph who was described as follows:
A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data: (a) 67% of the cabs in the city are Blue and 33% are Green. (b) A witness identified the cab as Green. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 50% of the time and failed 50% of the time. What is the probability that the cab involved in the accident was Green rather than Blue?
Since the statements are not mutually exclusive, the numbers (each from 0 to 100) need not sum to 100. Students were then asked to rate the likelihood of the following statements:
The example provides two sources of information: the base rates of the two types of cabs in the city (the “background information”) and the reliability of the witness who identified the cab as Green (the “case-specific information”). Thus, base-rate neglect problems may be thought of as problems involving multiple stimulus control. In the taxicab example the information provided by the witness is worthless (the witness’s ability to identify cab type is measured at chance level). Thus, the witness’s statement should exert no control and subjects should rely exclusively on the second source of information, the base rates. For the example given, the appropriate answer is simply that the probability the cab involved in the accident was Green is 33% (the base rate of Green cabs in the city). In fact, however, subjects ignore the base-rate information and judge the likelihood that the cab is green around 50%, or equal to the accuracy of the witness. Goodie and Fantino (1995, 1996, 1999a, 1999b) developed a behavioral analogue of the base-rate problem using a matchingto-sample (MTS) procedure. Some of their experiments and results are summarized in Fantino (2004). Basically, they found profound and persistent base-rate neglect even after several hundred trials. Would college students persist in committing base-rate neglect when it cost them money? In one condition, Goodie and Fantino (1995) compared the performance of students whose correct responses were reinforced with points not backed by money with that of students whose correct responses were reinforced with points backed by money. There was no significant difference between the two groups: base rates were neglected persistently.
If the conjunction statement is rated as more probable than either of the statements above it (typically “Ralph plays in a heavy-metal band for a hobby”), then the conjunction fallacy has been committed. We explored whether or not monetary incentives would lower incidence of the fallacy. The experiment was conducted with individual participants in the company of an experimenter. All participants received six conjunction problems (four involving Ralph with job and hobby combinations varied across problems plus the “Bill” and the “Linda” problems from Tversky and Kahneman, 1982). Participants were divided into six groups: (1) a standard control group that received the six problems with no feedback as to the correctness of their answers, nor monetary incentive, nor helpful hints regarding the solution; (2) a group given a hint but neither feedback nor incentive; (3) a group given a hint and feedback after each problem; (4) a group given feedback only; (5) a group given feedback after each trial and also earning $3 for each correct answer, payable at the end of the session; (6) a group identical to the previous group except that the $3 reward for each correct answer was given as soon as the correct answer was made. This last group was included to eliminate the possibility that participants did not believe they would be paid $3 for each correct answer (allowing the possibility of earning $18 in a few minutes). Indeed, for participants in this group the experimenter sat next to the participant while holding a stack of $1 bills. If participants understood the conjunction problem but merely required incentive and feedback to respond logically, then participants in the final two groups should not commit the fallacy or should refrain from doing so after repeated trials.
Ralph is 34 years old. He is intelligent though not especially creative, and his friends describe him as somewhat compulsive and dull. In college, he did well in the physical sciences but was weak in the humanities and social sciences. Please indicate the likelihood of each of the following statements about Ralph by entering a percentage on the line to the left of the statement—for example, “0” would be virtually impossible, and “100” virtually certain. You can think of the continuum of likelihood as looking like this: 0 Virtually impossible
100 Virtually certain
• Ralph is a building inspector. • Ralph plays in a heavy-metal band for a hobby. • Ralph is a building inspector who plays in a heavy-metal band for a hobby.
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Fig. 1. Conjunction errors as a function of task conditions and incentive.
The mean data are shown in Fig. 1. Overall, the fallacy was committed on 48% of the problems. Importantly, there was no difference across groups in the likelihood to commit the conjunction fallacy. Nor was there a decline in commission of the fallacy across the six trials (not shown). Here too incentive did not appear to affect performance. Thus, the three sets of studies from our laboratory suggest that hypothetical reinforcers may be viable surrogates for real monetary ones. This conclusion is also supported by the results of Johnson and Bickel (2002) who found comparable temporal discounting in human participants whether the incentives were real or hypothetical. However, Weiner (1977) reported higher rates of responding in his human participants when the reinforcer was real money than when hypothetical money served. Given the frequency with which hypothetical reinforcers are used, it is perhaps surprising that so few studies have compared their efficacy with that of non-hypothetical reinforcers. 3. The sharing game It is appropriate to differentiate between incentives intended to inspire subjects to greater effort or attention and incentives involved in specifically economic activities (e.g., see Camerer and Hogarth, 1999). None of the examples discussed above involved allocation of resources in economic games. There are studies suggesting that the nature of the allocations may in fact differ when real money is compared with hypothetical money (e.g., Camerer and Hogarth, 1999). Thus, we decided to explore this possibility using an economic game developed in our laboratory (the “Sharing Game”). In the Sharing Game, the player’s allocation decision determined both that player’s payoff and that of another (unseen, passive, and – in fact – non-existent) participant. The participant made repeated binary choices in which one outcome pair was higher for both players: one option (the “optimal” choice) resulted in higher amounts for both players, but gave the allocator slightly less than the other player; the other option (the “competitive” choice) gave lower amounts to both people, but gave the allocator a relative advantage over the other person (e.g., seven points for the allocator and nine for the other, versus five
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Fig. 2. One pair of choices presented to participants in the “Sharing Game”.
points for the allocator and three for the other). One exemplar is shown in Fig. 2. Each choice was immediately repeated once; this gave the participant the opportunity to alternate between the optimal and competitive options, thereby keeping payoffs equal, albeit not maximal, for the two players. Half the participants were told that the other player was a person and half that the other player was a computer. According to the “Computers Are Social Actors” or “CASA” model (Nass et al., 1993, 1994; Reeves and Nass, 1996), the social rules applying to humanhuman interaction apply equally to human-computer interaction, implying that Sharing Game participants might treat computer players the same way as “human” players. We did not know whether we would see such equality in our experiments though, since in the Sharing Game allocators do not interact directly with recipients. In contrast, the subjects and computers in the CASA experiments always participated in a two-way interaction, whether subjects were told that the computer was running a program or that it was acting as the medium through which another person communicated. We predicted that, due to the lack of involvement on the part of the computer in our experiments, participants would choose optimally more often when paired with a computer recipient. For half the participants the points earned had monetary value; for the others they did not. Finally, for half of the participants in one of our experiments the other player’s cumulative score was displayed, a factor that might have increased the competitive flavor of the task and, therefore, the choice of the smaller outcome. Based on prior research and theory, we would expect three modal allocation decision strategies. These strategies have a rough correspondence to strategies described by theories of social value orientation. For example, van Lange et al. (1997) describe “stable preferences for certain patterns of outcomes for oneself and others,” suggesting that fairness may motivate game playing for some participants. In particular, one of three classes of player is the “prosocial” player who tends to maximize joint payoffs and also minimize differences between the players’ payoffs. Such players should be likely to alternate between payoffs in the present procedure, although choosing the larger payoff for oneself with an even larger payoff for the other player may also be considered “prosocial.” The two
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other classes of player are the “individualist,” interested only in maximizing personal payoff, and the “competitor,” focusing on maximizing the difference between the players’ payoffs. One might expect the individualist to choose optimally, maximizing his payoff (and incidentally that of the other player). The “competitor” would be expected to choose the smaller amount as that choice maintains the greatest positive differential between his total and that of the other player. None of these three possible choice patterns, or “strategies” was explained to the participants. Would the distribution of strategies be affected by the economic context in which the game was played? A corollary of this question concerns the extent to which the strategies would appear to be relatively stable, as they might be if they reflected fundamental personality characteristics. Thus, we ask how choice was affected by monetary incentive and by other central aspects of the game (such as gender of participants, whether the other player was described as another student or as a computer, and whether the competitive aspects of the game were made more salient). In each of two experiments (Kennelly et al., submitted) we obtained the puzzling (to us) result that the nature of the other player (person or computer) had no effect on participants’ allocations. While this result may not be especially surprising to those who view a computer as a “social actor,” it appears bizarre to us that – with a computer as the other player – students would choose the competitive option when they are losing real money by doing so. Seeing the other player’s cumulative score (assessed in one experiment only) also had no effect on allocations. The major finding of both studies, as shown in Figs. 3 and 4, was the large effect of monetary incentive on participants’ allocations. Participants’ choices produced a trimodal distribution with the three modes corresponding to the three straightforward strategies: equalizing payoffs (the mode, at 50% on Fig. 3a); always selecting the optimal option by choosing the larger payoffs, the second mode at 100% on Fig. 3a; or always selecting the competitive option by choosing the smaller payoffs, the third mode at 0% on Fig. 3a. When the participants were divided according to whether or not points represented monetary reward, a different picture emerged. Fig. 3b, for participants in the “money” condition, shows a bimodal distribution with optimal responding now the mode, though more participants continued to approximate equalizing, rather than maximizing, payoffs. The third mode seen at 0% in Fig. 3a, representing extreme competition, is absent. Fig. 3c shows that when only participants in the “no money” condition are considered, a third pattern emerged. Again we obtained a bimodal distribution, but now the modes are at 50% (equalizing payoffs) and at 0% (extreme competition); the mode at 100%, seen in Fig. 3a and b and representing optimal choice, is absent. These results indicated that students chose more optimally in the monetary condition, a conclusion that did not bode well for researching economic games on a shoestring budget. Thus, we decided to repeat the experiment to confirm this conclusion. We had noted, however, that the instructions for the experiment had a game-playing flavor that might have increased the
Fig. 3. Number of participants and the percentage of trials in which they chose the optimal option on the “Sharing Game”: (a) data for all participants; (b) data for participants whose points were backed by money (“Money Participants”); (c) data for participants whose points were not backed by money (“No Money Participants”).
number of competitive, non-optimal choices. Indeed, 46 of our 238 participants reported that hearing and/or reading the words “game” and/or “player” influenced their decision to choose competitively. Thus, we repeated the experiment with more neutral instructions. The replication afforded the opportunity to ascertain whether monetary rewards would again lead to more optimal decisions and whether participants’ decisions would again be unaffected by the nature of the other player (person or computer). As a comparison of the results in Figs. 3 and 4 shows, the changed instructions affected the results. The trimodal distribution is gone (compare Fig. 3a and 4a) replaced by a bimodal distribution of allocations (Fig. 4a). By eliminating the instructions suggesting a game, we also eliminated the mode at 0% that would indicate extreme competitiveness. As in the first experiment, the mode is at 50%, suggesting a tendency to equalize payoffs. A secondary mode is seen at 100%, indicating choice of the optimal option. The effect of monetary incentive remains. As shown in Fig. 4b, when points were exchangeable for money, the modal choice was the optimal one (mode at 100%). When earned points were not exchangeable for money, there was a unimodal
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4. Future directions: How about altruism? The Sharing Game permits study of a wide variety of decisions. One of particular interest is the study of altruism (e.g., Rachlin, 2002; Fantino and Stolarz-Fantino, 2002). We are currently offering students a number of decisions including ones with an altruistic option. For example, on one problem the student has the option of receiving 50 cents while the other player also receives 50 cents OR of receiving nothing while the other player receives $5.00. What proportion of students would select altruistically, choosing nothing for themselves but bestowing a small windfall on an anonymous other? Shawn Charlton has collected data in our laboratory on a similar problem, but with hypothetical rewards; he found that about 20% of students selected altruistically. But the acid test for altruism comes when real money is involved. Since funds to bestow on participants are limited, another future direction is finding meaningful alternatives to money as commodities for allocation in economic games. One promising candidate is time. 5. Why not time instead of money?
Fig. 4. Number of participants and the percentage of trials in which they chose the optimal option on the “Sharing Game” with neutral (not game-oriented) instructions: (a) data for all participants; (b) data for participants whose points were backed by money (“Money Participants”); (c) data for participants whose points were not backed by money (“No Money Participants”).
distribution with the mode at 50% (Fig. 4c). In conclusion, motivational context matters in the Sharing Game: our results show that, under certain conditions, a typical participant may carry out an equitable selection strategy over either more optimal or more competitive strategies, and that the allocation distribution produced will depend critically on the presence or absence of both monetary incentives and of instructions suggesting that the task is a game. Although the distributions of allocations could be seen as consistent with theories of social value orientation as discussed above (e.g., van Lange et al., 1997), they do not appear as the required “stable preferences for certain patterns of outcomes for oneself and others” that van Lange et al. discuss. Instead, the allocation distributions varied as a function of factors such as monetary incentive and instructional context while being unaffected by the nature of the other participant (person or computer). Although the results discussed above are based on experiments using a between-subjects design, ongoing research in our laboratory is finding the same changes in allocation distributions as a function of incentive with a within-subjects design.
Money is a powerful reinforcer. Our results from the Sharing Game suggest that hypothetical rewards cannot be assumed to have a comparable effect on decisions in economic games. In fact, a recent review by Lea and Webley (2006) suggests that money may even have addictive properties, comparable to that of some drugs. Nonetheless, Gaitan et al. (submitted) explored an alternative to real money that may be just as motivating, but without the cost to the experimenters. This alternative is time off from a tedious task. We selected a task in which participants judged whether computer displays were random or meaningful. In prior research with this image-sorting task by Gaitan, participants routinely complained that the task was tedious. Thus, we decided to compare participants’ allocations on two classic economic games under three motivational conditions. Participants allocated one of three resources: (1) hypothetical money; (2) real money; or (3) time off from this image-sorting task. The expectation was that participants would make more economically optimal allocations with real money than with hypothetical money. The question of central interest was whether allocation of time off from a tedious task would more closely resemble allocations in the hypothetical money or real money conditions. If the allocations of time off were comparable to those of real money, then future experiments involving allocations in economic games may be conducted with some assurance of external validity but without great monetary cost. In addition, use of a novel resource would permit assessment of the generality of findings with the allocation of money with a different commodity (time). For example, are the nonoptimal allocations found consistently with money also found with time as the allocated resource? The two games studied were the Dictator game (DG) and the Ultimatum Game (UG) (Forsythe et al., 1994; Guth et al., 1982). Choices in these games are thought to reveal basic characteristics of the ways in which participants allocate resources between themselves and another person and, in the case of the
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UG, whether the proposed distributions are deemed acceptable by a recipient. In the UG, one student proposes a distribution of resources (for example, if $10, $6 for him and $4 for the other player). If the other player accepts, the $6–$4 split becomes reality. If the other player rejects the offer, neither gets anything (no negotiation is possible). In the DG, whatever the proposing participant proposes becomes reality (the second player is passive). The rational (or optimal) allocation in the DG is to keep as much of the resources as possible, namely all; in the UG the rational or optimal allocation is the smallest possible positive offer (Camerer, 2003, pp. 43–44). In terms of the recipient, in the UG the recipient should accept any non-zero offer. Participants do not typically allocate optimally however (nor do recipients typically accept very low non-zero offers). Students were generally studied in groups of eight. All students in a given group were participants in the same reward condition: real money, hypothetical money, or time off. Students were assigned partners; however none knew which of the other seven participants was his/her partner, preserving a degree of anonymity. First, students were introduced to the image-sorting task, which they performed for one minute. Then they were told that, after a brief question period, they would spend the remainder of the hour (50 min) working on this task. During the question period, the students were asked to allocate $50 real money, $50 hypothetical money or 50 min (depending on the condition) between themselves and their partners. Participants in the real money condition were informed that the money was probabilistic; they played a game of chance in which they had about a 1/3 chance to actually obtain the money, in which case they received the amount they had been allocated. Half of the proposers were in the UG and half in the DG. The main results are shown in Fig. 5a–c. Resource allocation was comparable for the UG and DG for all three-resource types (“Hypothetical”, “Money”, and “Time”). The central question asked in this study was whether or not time off from a tedious task could serve as an effective resource, comparable to real money, in economic games involving resource allocation. The results shown in Fig. 5 answer this question affirmatively. Participants tended to keep a much larger amount of the resource when time off from a tedious task was the resource than when hypothetical money was the resource. Indeed, for the values studied, time off led to greater retention of resources than real money. Of course it is difficult to compare rewards that constitute different currencies. Although “time is money,” how much money a given amount of time represents will depend on the context and the individual. The general point is that time off can serve as a meaningful reinforcer, one that can be utilized in lieu of real money without the putative (if controversial) shortcomings of hypothetical reinforcers and without the cost of real money. That being said, there are procedures and theories for integrating and/or equating time and money. For example, time can be integrated into the unit-price functions of behavioral economics. Although the usual way of looking at unit price involves response effort and magnitude of reward as in manipulations of fixed-ratio (FR) size and reinforcer magnitude, Tsunematsu (2001) compared demand curves for food under effort-cost and time-cost
Fig. 5. Proportion of resources kept in offers in the Ultimatum and Dictator Games when different resources were divided: (a) hypothetical money; (b) probabilistic real money; (c) time off from a tedious image-sorting task. In each case the histogram displays of proportion of subjects who proposed to keep the proportion shown on the abscissa.
conditions. This study found that food consumption as a function of time-based unit price showed “moderate convergence” on a single demand function. However, a more fine-grained analysis indicated that food intake was more sensitive to effort than to time. In any event, these results show that it would be feasible to conduct a study comparing demand curves for money and time. Studies of temporal discounting also integrate the influence of money and time in the sense that, the more delayed the monetary reward, the less it is valued (for a recent review see Charlton, 2006). However, in the present work it is time off from an aversive task that is the relevant commodity. Another sense in which monetary factors may influence decisions in economic games relates to the income or wealth of the participants. This clearly requires additional study. However, the slight extant literature provides no evidence that wealth
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influences decisions in these games. For example, Henrich et al. (2005) found no evidence that wealth relative to others of their community influenced participants’ decisions in several economic games, studied in a variety of diverse cultures. Our main goal was to show that time off from an aversive task could be a powerful reinforcer, comparable to money. For most purposes it would not be necessary to equate the potency of a particular amount of money and a particular amount of time off. However, a simple process of titration could do this. For example, in our study time off from a tedious task was actually more potent than money for the values we selected. In order to equate the values, one could simply collect pilot data increasing the amount of money (or decreasing the time off) until the reinforcers were equal in value. Then the main study could be conducted with the equated values. 6. Conclusions Thus, time-off from a tedious task appears to function effectively as a resource to be allocated in economic games. For cultures in which “Time is money,” the efficacy of time off as a valued commodity should not be surprising. The present results have three central conclusions. First, real money is more effective than hypothetical money in terms of promoting closer approximations to optimal allocation strategies in economic games. Thus, researchers cannot use hypothetical rewards and assume that their results would be comparable to results with more meaningful rewards. It appears that the economists who have been making this argument are on firm ground (e.g., Hertwig and Ortmann, 2001). Second, time-off can be utilized in studies of decision-making in economic games without incurring the monetary costs involved when real money is used and without incurring the criticism leveled against hypothetical resources, namely that they are not effective or ecologically valid resources. Third, the results extend the generality of findings with real money. Many prior studies have shown that students make non-optimal allocations in economic games when money is the commodity. The present results show that the same conclusion is warranted when a different valuable commodity – time – is allocated. Since it appears that the more effective the reinforcer the more optimal the behavior, the possibility is raised that with sufficiently powerful reinforcers, allocation decisions might more closely approach optimality. Acknowledgements We thank Amonty Parsons for yeoman assistance in collecting pilot data. National Institute of Mental Health Grant MH57127 supported the research and manuscript preparation. References Case, D.A., Fantino, E., 1989. Instructions and reinforcement in the observing behavior of adults and children. Learn. Motiv. 20, 373–412. Case, D.A., Fantino, E., Wixted, J., 1985. Human observing: maintained by negative informative stimuli only if correlated with improvement in response efficiency. J. Exp. Anal. Behav. 43, 289–300.
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Stolarz-Fantino, S., Fantino, E., Zizzo, D., Wen, J., 2003. The conjunction effect: new evidence for robustness. Am. J. Psychol. 116, 15–34. Tsunematsu, S., 2001. Effort- and time-cost effects on demand curves for food by pigeons under short session closed economies. Behav. Process. 53, 47–56. Tversky, A., Kahneman, D., 1982. Evidential impact of base rates. In: Kahneman, D., Slovic, P., Tversky, A. (Eds.), Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge.
Tversky, A., Kahneman, D., 1983. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychol. Rev. 90, 293–315. Van Lange, P.A., deBruin, E.M.N., Otten, W., Joireman, J.A., 1997. Development of prosocial, individualistic, and competitive orientations: theory and preliminary evidence. J. Personal. Soc. Psychol. 73, 733–746. Weiner, H., 1977. An operant analysis of human altruistic responding. J. Exp. Anal. Behav. 27, 515–528.
How reinforcer type affects choice in economic games Edmund Fantino ∗ , Santino Gaitan, Art Kennelly, Stephanie Stolarz-Fantino University of California, San Diego, United States Received 25 August 2006; received in revised form 8 December 2006; accepted 8 December 2006
Abstract Behavioral economists stress that experiments on judgment and decision-making using economic games should be played with real money if the results are to have generality. Behavior analysts have sometimes disputed this contention and have reported results in which hypothetical rewards and real money have produced comparable outcomes. We review studies that have compared hypothetical and real money and discuss the results of two relevant experiments. In the first, using the Sharing Game developed in our laboratory, subjects’ choices differed markedly depending on whether the rewards were real or hypothetical. In the second, using the Ultimatum and Dictator Games, we again found sharp differences between real and hypothetical rewards. However, this study also showed that time off from a tedious task could serve as a reinforcer every bit as potent as money. In addition to their empirical and theoretical contributions, these studies make the methodological point that meaningful studies may be conducted with economic games without spending money: time off from a tedious task can serve as a powerful reward. © 2007 Elsevier B.V. All rights reserved. Keywords: Altruism; Economic games; Optimality; Reinforcer type; Sharing game
1. Introduction
2. Comparing monetary and non-monetary incentives
Studies with meaningful payoffs and a sufficient number of subjects can be expensive to conduct if the payoffs are made in real money. Thus, psychologists have often used hypothetical money as the payoff in the expectation that the general pattern of results would be the same as if real money were distributed. Economists have used real money and have asserted that results with hypothetical money may not have external validity. These differing viewpoints were discussed at length in the target article and commentaries in Hertwig and Ortmann (2001). Fantino and Stolarz-Fantino (2001) cited several studies from their laboratory suggesting that comparable results are obtained with points backed or not backed by real money. Studies in which results with hypothetical and real money were comparable include those of Case and Fantino (1989) on the conditions under which information reinforces observing behavior, Goodie and Fantino (1995) on a behavioral analog of base-rate neglect, and StolarzFantino et al. (2003) on the effects of monetary reinforcement and feedback on the conjunction fallacy.
Case and Fantino (1989)’s study was one in a series of studies from our laboratory, primarily with human subjects, that explored the conditions under which adults and children would make observing responses—that is, responses the only function of which was to produce stimuli correlated with the schedule of reinforcement in effect. The results of these studies, along with those from other laboratories, notably that of Dinsmoor with pigeons as subjects (e.g., Dinsmoor, 1983; Dinsmoor et al., 1972), suggested that observing was not maintained by production of a stimulus correlated with the absence of reinforcement but only by the production of a stimulus differentially correlated with reinforcement. In other words, an informative stimulus maintained observing only when the stimulus was correlated with a richer reinforcement environment than that present in the absence of the stimulus. These results supported versions of the conditioned reinforcement account of observing but were incompatible with accounts stressing that information per se was reinforcing (for a review of both positions see Fantino, 1977). The human studies supporting the conditioned-reinforcement account of observing used points – not money – as a reinforcer (e.g., Case et al., 1985; Fantino and Case, 1983), though Fantino et al. (1983) used marbles with some of their children. Perhaps the reinforcing potency of an (informative) extinction stimulus would become evident if the students’ responding resulted in
∗ Corresponding author at: Department of Psychology, 0109, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0109, United States. Tel.: +1 858 534 3927; fax: +1 858 534 7190. E-mail address: [email protected] (E. Fantino).
0376-6357/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2007.02.001
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points backed by real money. Thus, Case and Fantino (1989) included a study in which points were not backed by money in one condition, points were each worth 5 cents in a second condition, and points were each worth 25 cents in a third condition. The results showed that the incentive had no discernible effect on rate of observing. In the critical condition, preference for the informative S- was pitted against preference for a totally uninformative stimulus. No matter what the incentive, preference for the informative S- was significantly below .50. Moreover, in none of the conditions was a systematic effect of incentive evident. Avoidance of even useful information is central to base-rate neglect, in which, when predicting an event, educated students neglect the molar frequencies of the possibilities and instead overemphasize case-specific information (e.g., Kahneman and Tversky, 1973). A classic example is adapted from Tversky and Kahneman (1982):
Our third and final example comes from a study on factors controlling the conjunction fallacy, another logical fallacy discussed by Tversky and Kahneman (1983). Our version of the fallacy (Experiment 5 in Stolarz-Fantino et al., 2003) concerned an individual named Ralph who was described as follows:
A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data: (a) 67% of the cabs in the city are Blue and 33% are Green. (b) A witness identified the cab as Green. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 50% of the time and failed 50% of the time. What is the probability that the cab involved in the accident was Green rather than Blue?
Since the statements are not mutually exclusive, the numbers (each from 0 to 100) need not sum to 100. Students were then asked to rate the likelihood of the following statements:
The example provides two sources of information: the base rates of the two types of cabs in the city (the “background information”) and the reliability of the witness who identified the cab as Green (the “case-specific information”). Thus, base-rate neglect problems may be thought of as problems involving multiple stimulus control. In the taxicab example the information provided by the witness is worthless (the witness’s ability to identify cab type is measured at chance level). Thus, the witness’s statement should exert no control and subjects should rely exclusively on the second source of information, the base rates. For the example given, the appropriate answer is simply that the probability the cab involved in the accident was Green is 33% (the base rate of Green cabs in the city). In fact, however, subjects ignore the base-rate information and judge the likelihood that the cab is green around 50%, or equal to the accuracy of the witness. Goodie and Fantino (1995, 1996, 1999a, 1999b) developed a behavioral analogue of the base-rate problem using a matchingto-sample (MTS) procedure. Some of their experiments and results are summarized in Fantino (2004). Basically, they found profound and persistent base-rate neglect even after several hundred trials. Would college students persist in committing base-rate neglect when it cost them money? In one condition, Goodie and Fantino (1995) compared the performance of students whose correct responses were reinforced with points not backed by money with that of students whose correct responses were reinforced with points backed by money. There was no significant difference between the two groups: base rates were neglected persistently.
If the conjunction statement is rated as more probable than either of the statements above it (typically “Ralph plays in a heavy-metal band for a hobby”), then the conjunction fallacy has been committed. We explored whether or not monetary incentives would lower incidence of the fallacy. The experiment was conducted with individual participants in the company of an experimenter. All participants received six conjunction problems (four involving Ralph with job and hobby combinations varied across problems plus the “Bill” and the “Linda” problems from Tversky and Kahneman, 1982). Participants were divided into six groups: (1) a standard control group that received the six problems with no feedback as to the correctness of their answers, nor monetary incentive, nor helpful hints regarding the solution; (2) a group given a hint but neither feedback nor incentive; (3) a group given a hint and feedback after each problem; (4) a group given feedback only; (5) a group given feedback after each trial and also earning $3 for each correct answer, payable at the end of the session; (6) a group identical to the previous group except that the $3 reward for each correct answer was given as soon as the correct answer was made. This last group was included to eliminate the possibility that participants did not believe they would be paid $3 for each correct answer (allowing the possibility of earning $18 in a few minutes). Indeed, for participants in this group the experimenter sat next to the participant while holding a stack of $1 bills. If participants understood the conjunction problem but merely required incentive and feedback to respond logically, then participants in the final two groups should not commit the fallacy or should refrain from doing so after repeated trials.
Ralph is 34 years old. He is intelligent though not especially creative, and his friends describe him as somewhat compulsive and dull. In college, he did well in the physical sciences but was weak in the humanities and social sciences. Please indicate the likelihood of each of the following statements about Ralph by entering a percentage on the line to the left of the statement—for example, “0” would be virtually impossible, and “100” virtually certain. You can think of the continuum of likelihood as looking like this: 0 Virtually impossible
100 Virtually certain
• Ralph is a building inspector. • Ralph plays in a heavy-metal band for a hobby. • Ralph is a building inspector who plays in a heavy-metal band for a hobby.
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Fig. 1. Conjunction errors as a function of task conditions and incentive.
The mean data are shown in Fig. 1. Overall, the fallacy was committed on 48% of the problems. Importantly, there was no difference across groups in the likelihood to commit the conjunction fallacy. Nor was there a decline in commission of the fallacy across the six trials (not shown). Here too incentive did not appear to affect performance. Thus, the three sets of studies from our laboratory suggest that hypothetical reinforcers may be viable surrogates for real monetary ones. This conclusion is also supported by the results of Johnson and Bickel (2002) who found comparable temporal discounting in human participants whether the incentives were real or hypothetical. However, Weiner (1977) reported higher rates of responding in his human participants when the reinforcer was real money than when hypothetical money served. Given the frequency with which hypothetical reinforcers are used, it is perhaps surprising that so few studies have compared their efficacy with that of non-hypothetical reinforcers. 3. The sharing game It is appropriate to differentiate between incentives intended to inspire subjects to greater effort or attention and incentives involved in specifically economic activities (e.g., see Camerer and Hogarth, 1999). None of the examples discussed above involved allocation of resources in economic games. There are studies suggesting that the nature of the allocations may in fact differ when real money is compared with hypothetical money (e.g., Camerer and Hogarth, 1999). Thus, we decided to explore this possibility using an economic game developed in our laboratory (the “Sharing Game”). In the Sharing Game, the player’s allocation decision determined both that player’s payoff and that of another (unseen, passive, and – in fact – non-existent) participant. The participant made repeated binary choices in which one outcome pair was higher for both players: one option (the “optimal” choice) resulted in higher amounts for both players, but gave the allocator slightly less than the other player; the other option (the “competitive” choice) gave lower amounts to both people, but gave the allocator a relative advantage over the other person (e.g., seven points for the allocator and nine for the other, versus five
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Fig. 2. One pair of choices presented to participants in the “Sharing Game”.
points for the allocator and three for the other). One exemplar is shown in Fig. 2. Each choice was immediately repeated once; this gave the participant the opportunity to alternate between the optimal and competitive options, thereby keeping payoffs equal, albeit not maximal, for the two players. Half the participants were told that the other player was a person and half that the other player was a computer. According to the “Computers Are Social Actors” or “CASA” model (Nass et al., 1993, 1994; Reeves and Nass, 1996), the social rules applying to humanhuman interaction apply equally to human-computer interaction, implying that Sharing Game participants might treat computer players the same way as “human” players. We did not know whether we would see such equality in our experiments though, since in the Sharing Game allocators do not interact directly with recipients. In contrast, the subjects and computers in the CASA experiments always participated in a two-way interaction, whether subjects were told that the computer was running a program or that it was acting as the medium through which another person communicated. We predicted that, due to the lack of involvement on the part of the computer in our experiments, participants would choose optimally more often when paired with a computer recipient. For half the participants the points earned had monetary value; for the others they did not. Finally, for half of the participants in one of our experiments the other player’s cumulative score was displayed, a factor that might have increased the competitive flavor of the task and, therefore, the choice of the smaller outcome. Based on prior research and theory, we would expect three modal allocation decision strategies. These strategies have a rough correspondence to strategies described by theories of social value orientation. For example, van Lange et al. (1997) describe “stable preferences for certain patterns of outcomes for oneself and others,” suggesting that fairness may motivate game playing for some participants. In particular, one of three classes of player is the “prosocial” player who tends to maximize joint payoffs and also minimize differences between the players’ payoffs. Such players should be likely to alternate between payoffs in the present procedure, although choosing the larger payoff for oneself with an even larger payoff for the other player may also be considered “prosocial.” The two
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other classes of player are the “individualist,” interested only in maximizing personal payoff, and the “competitor,” focusing on maximizing the difference between the players’ payoffs. One might expect the individualist to choose optimally, maximizing his payoff (and incidentally that of the other player). The “competitor” would be expected to choose the smaller amount as that choice maintains the greatest positive differential between his total and that of the other player. None of these three possible choice patterns, or “strategies” was explained to the participants. Would the distribution of strategies be affected by the economic context in which the game was played? A corollary of this question concerns the extent to which the strategies would appear to be relatively stable, as they might be if they reflected fundamental personality characteristics. Thus, we ask how choice was affected by monetary incentive and by other central aspects of the game (such as gender of participants, whether the other player was described as another student or as a computer, and whether the competitive aspects of the game were made more salient). In each of two experiments (Kennelly et al., submitted) we obtained the puzzling (to us) result that the nature of the other player (person or computer) had no effect on participants’ allocations. While this result may not be especially surprising to those who view a computer as a “social actor,” it appears bizarre to us that – with a computer as the other player – students would choose the competitive option when they are losing real money by doing so. Seeing the other player’s cumulative score (assessed in one experiment only) also had no effect on allocations. The major finding of both studies, as shown in Figs. 3 and 4, was the large effect of monetary incentive on participants’ allocations. Participants’ choices produced a trimodal distribution with the three modes corresponding to the three straightforward strategies: equalizing payoffs (the mode, at 50% on Fig. 3a); always selecting the optimal option by choosing the larger payoffs, the second mode at 100% on Fig. 3a; or always selecting the competitive option by choosing the smaller payoffs, the third mode at 0% on Fig. 3a. When the participants were divided according to whether or not points represented monetary reward, a different picture emerged. Fig. 3b, for participants in the “money” condition, shows a bimodal distribution with optimal responding now the mode, though more participants continued to approximate equalizing, rather than maximizing, payoffs. The third mode seen at 0% in Fig. 3a, representing extreme competition, is absent. Fig. 3c shows that when only participants in the “no money” condition are considered, a third pattern emerged. Again we obtained a bimodal distribution, but now the modes are at 50% (equalizing payoffs) and at 0% (extreme competition); the mode at 100%, seen in Fig. 3a and b and representing optimal choice, is absent. These results indicated that students chose more optimally in the monetary condition, a conclusion that did not bode well for researching economic games on a shoestring budget. Thus, we decided to repeat the experiment to confirm this conclusion. We had noted, however, that the instructions for the experiment had a game-playing flavor that might have increased the
Fig. 3. Number of participants and the percentage of trials in which they chose the optimal option on the “Sharing Game”: (a) data for all participants; (b) data for participants whose points were backed by money (“Money Participants”); (c) data for participants whose points were not backed by money (“No Money Participants”).
number of competitive, non-optimal choices. Indeed, 46 of our 238 participants reported that hearing and/or reading the words “game” and/or “player” influenced their decision to choose competitively. Thus, we repeated the experiment with more neutral instructions. The replication afforded the opportunity to ascertain whether monetary rewards would again lead to more optimal decisions and whether participants’ decisions would again be unaffected by the nature of the other player (person or computer). As a comparison of the results in Figs. 3 and 4 shows, the changed instructions affected the results. The trimodal distribution is gone (compare Fig. 3a and 4a) replaced by a bimodal distribution of allocations (Fig. 4a). By eliminating the instructions suggesting a game, we also eliminated the mode at 0% that would indicate extreme competitiveness. As in the first experiment, the mode is at 50%, suggesting a tendency to equalize payoffs. A secondary mode is seen at 100%, indicating choice of the optimal option. The effect of monetary incentive remains. As shown in Fig. 4b, when points were exchangeable for money, the modal choice was the optimal one (mode at 100%). When earned points were not exchangeable for money, there was a unimodal
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4. Future directions: How about altruism? The Sharing Game permits study of a wide variety of decisions. One of particular interest is the study of altruism (e.g., Rachlin, 2002; Fantino and Stolarz-Fantino, 2002). We are currently offering students a number of decisions including ones with an altruistic option. For example, on one problem the student has the option of receiving 50 cents while the other player also receives 50 cents OR of receiving nothing while the other player receives $5.00. What proportion of students would select altruistically, choosing nothing for themselves but bestowing a small windfall on an anonymous other? Shawn Charlton has collected data in our laboratory on a similar problem, but with hypothetical rewards; he found that about 20% of students selected altruistically. But the acid test for altruism comes when real money is involved. Since funds to bestow on participants are limited, another future direction is finding meaningful alternatives to money as commodities for allocation in economic games. One promising candidate is time. 5. Why not time instead of money?
Fig. 4. Number of participants and the percentage of trials in which they chose the optimal option on the “Sharing Game” with neutral (not game-oriented) instructions: (a) data for all participants; (b) data for participants whose points were backed by money (“Money Participants”); (c) data for participants whose points were not backed by money (“No Money Participants”).
distribution with the mode at 50% (Fig. 4c). In conclusion, motivational context matters in the Sharing Game: our results show that, under certain conditions, a typical participant may carry out an equitable selection strategy over either more optimal or more competitive strategies, and that the allocation distribution produced will depend critically on the presence or absence of both monetary incentives and of instructions suggesting that the task is a game. Although the distributions of allocations could be seen as consistent with theories of social value orientation as discussed above (e.g., van Lange et al., 1997), they do not appear as the required “stable preferences for certain patterns of outcomes for oneself and others” that van Lange et al. discuss. Instead, the allocation distributions varied as a function of factors such as monetary incentive and instructional context while being unaffected by the nature of the other participant (person or computer). Although the results discussed above are based on experiments using a between-subjects design, ongoing research in our laboratory is finding the same changes in allocation distributions as a function of incentive with a within-subjects design.
Money is a powerful reinforcer. Our results from the Sharing Game suggest that hypothetical rewards cannot be assumed to have a comparable effect on decisions in economic games. In fact, a recent review by Lea and Webley (2006) suggests that money may even have addictive properties, comparable to that of some drugs. Nonetheless, Gaitan et al. (submitted) explored an alternative to real money that may be just as motivating, but without the cost to the experimenters. This alternative is time off from a tedious task. We selected a task in which participants judged whether computer displays were random or meaningful. In prior research with this image-sorting task by Gaitan, participants routinely complained that the task was tedious. Thus, we decided to compare participants’ allocations on two classic economic games under three motivational conditions. Participants allocated one of three resources: (1) hypothetical money; (2) real money; or (3) time off from this image-sorting task. The expectation was that participants would make more economically optimal allocations with real money than with hypothetical money. The question of central interest was whether allocation of time off from a tedious task would more closely resemble allocations in the hypothetical money or real money conditions. If the allocations of time off were comparable to those of real money, then future experiments involving allocations in economic games may be conducted with some assurance of external validity but without great monetary cost. In addition, use of a novel resource would permit assessment of the generality of findings with the allocation of money with a different commodity (time). For example, are the nonoptimal allocations found consistently with money also found with time as the allocated resource? The two games studied were the Dictator game (DG) and the Ultimatum Game (UG) (Forsythe et al., 1994; Guth et al., 1982). Choices in these games are thought to reveal basic characteristics of the ways in which participants allocate resources between themselves and another person and, in the case of the
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UG, whether the proposed distributions are deemed acceptable by a recipient. In the UG, one student proposes a distribution of resources (for example, if $10, $6 for him and $4 for the other player). If the other player accepts, the $6–$4 split becomes reality. If the other player rejects the offer, neither gets anything (no negotiation is possible). In the DG, whatever the proposing participant proposes becomes reality (the second player is passive). The rational (or optimal) allocation in the DG is to keep as much of the resources as possible, namely all; in the UG the rational or optimal allocation is the smallest possible positive offer (Camerer, 2003, pp. 43–44). In terms of the recipient, in the UG the recipient should accept any non-zero offer. Participants do not typically allocate optimally however (nor do recipients typically accept very low non-zero offers). Students were generally studied in groups of eight. All students in a given group were participants in the same reward condition: real money, hypothetical money, or time off. Students were assigned partners; however none knew which of the other seven participants was his/her partner, preserving a degree of anonymity. First, students were introduced to the image-sorting task, which they performed for one minute. Then they were told that, after a brief question period, they would spend the remainder of the hour (50 min) working on this task. During the question period, the students were asked to allocate $50 real money, $50 hypothetical money or 50 min (depending on the condition) between themselves and their partners. Participants in the real money condition were informed that the money was probabilistic; they played a game of chance in which they had about a 1/3 chance to actually obtain the money, in which case they received the amount they had been allocated. Half of the proposers were in the UG and half in the DG. The main results are shown in Fig. 5a–c. Resource allocation was comparable for the UG and DG for all three-resource types (“Hypothetical”, “Money”, and “Time”). The central question asked in this study was whether or not time off from a tedious task could serve as an effective resource, comparable to real money, in economic games involving resource allocation. The results shown in Fig. 5 answer this question affirmatively. Participants tended to keep a much larger amount of the resource when time off from a tedious task was the resource than when hypothetical money was the resource. Indeed, for the values studied, time off led to greater retention of resources than real money. Of course it is difficult to compare rewards that constitute different currencies. Although “time is money,” how much money a given amount of time represents will depend on the context and the individual. The general point is that time off can serve as a meaningful reinforcer, one that can be utilized in lieu of real money without the putative (if controversial) shortcomings of hypothetical reinforcers and without the cost of real money. That being said, there are procedures and theories for integrating and/or equating time and money. For example, time can be integrated into the unit-price functions of behavioral economics. Although the usual way of looking at unit price involves response effort and magnitude of reward as in manipulations of fixed-ratio (FR) size and reinforcer magnitude, Tsunematsu (2001) compared demand curves for food under effort-cost and time-cost
Fig. 5. Proportion of resources kept in offers in the Ultimatum and Dictator Games when different resources were divided: (a) hypothetical money; (b) probabilistic real money; (c) time off from a tedious image-sorting task. In each case the histogram displays of proportion of subjects who proposed to keep the proportion shown on the abscissa.
conditions. This study found that food consumption as a function of time-based unit price showed “moderate convergence” on a single demand function. However, a more fine-grained analysis indicated that food intake was more sensitive to effort than to time. In any event, these results show that it would be feasible to conduct a study comparing demand curves for money and time. Studies of temporal discounting also integrate the influence of money and time in the sense that, the more delayed the monetary reward, the less it is valued (for a recent review see Charlton, 2006). However, in the present work it is time off from an aversive task that is the relevant commodity. Another sense in which monetary factors may influence decisions in economic games relates to the income or wealth of the participants. This clearly requires additional study. However, the slight extant literature provides no evidence that wealth
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influences decisions in these games. For example, Henrich et al. (2005) found no evidence that wealth relative to others of their community influenced participants’ decisions in several economic games, studied in a variety of diverse cultures. Our main goal was to show that time off from an aversive task could be a powerful reinforcer, comparable to money. For most purposes it would not be necessary to equate the potency of a particular amount of money and a particular amount of time off. However, a simple process of titration could do this. For example, in our study time off from a tedious task was actually more potent than money for the values we selected. In order to equate the values, one could simply collect pilot data increasing the amount of money (or decreasing the time off) until the reinforcers were equal in value. Then the main study could be conducted with the equated values. 6. Conclusions Thus, time-off from a tedious task appears to function effectively as a resource to be allocated in economic games. For cultures in which “Time is money,” the efficacy of time off as a valued commodity should not be surprising. The present results have three central conclusions. First, real money is more effective than hypothetical money in terms of promoting closer approximations to optimal allocation strategies in economic games. Thus, researchers cannot use hypothetical rewards and assume that their results would be comparable to results with more meaningful rewards. It appears that the economists who have been making this argument are on firm ground (e.g., Hertwig and Ortmann, 2001). Second, time-off can be utilized in studies of decision-making in economic games without incurring the monetary costs involved when real money is used and without incurring the criticism leveled against hypothetical resources, namely that they are not effective or ecologically valid resources. Third, the results extend the generality of findings with real money. Many prior studies have shown that students make non-optimal allocations in economic games when money is the commodity. The present results show that the same conclusion is warranted when a different valuable commodity – time – is allocated. Since it appears that the more effective the reinforcer the more optimal the behavior, the possibility is raised that with sufficiently powerful reinforcers, allocation decisions might more closely approach optimality. Acknowledgements We thank Amonty Parsons for yeoman assistance in collecting pilot data. National Institute of Mental Health Grant MH57127 supported the research and manuscript preparation. References Case, D.A., Fantino, E., 1989. Instructions and reinforcement in the observing behavior of adults and children. Learn. Motiv. 20, 373–412. Case, D.A., Fantino, E., Wixted, J., 1985. Human observing: maintained by negative informative stimuli only if correlated with improvement in response efficiency. J. Exp. Anal. Behav. 43, 289–300.
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