• JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2005, 83, 1–13 NUMBER 1 (JANUARY)


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    • Abstract: JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2005, 83, 1–13 NUMBER 1 (JANUARY)THE SUNK COST EFFECT IN PIGEONS AND HUMANSA NTON D. N AVARRO AND E DMUND F ANTINO

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JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2005, 83, 1–13 NUMBER 1 (JANUARY)
THE SUNK COST EFFECT IN PIGEONS AND HUMANS
A NTON D. N AVARRO AND E DMUND F ANTINO
UNIVERSIT Y OF CALIFORNIA SAN DIEGO
The sunk cost effect is the increased tendency to persist in an endeavor once an investment of
money, effort, or time has been made. To date, humans are the only animal in which this effect has
been observed unambiguously. We developed a behavior-analytic model of the sunk cost effect to
explore the potential for this behavior in pigeons as well as in humans. Each trial started out with
a short expected ratio, but on some trials assumed a longer expected ratio part way through the
trial. Subjects had the (usually preferable) option of ‘‘escaping’’ the trial if the longer expected ratio
had come into effect in order to bring on a new trial that again had a short expected ratio. In
Experiments 1 through 3, we manipulated two independent variables that we hypothesized would
affect the pigeons’ ability to discriminate the increase in the expected ratio within a trial: (a) the
presence or absence of stimuli that signal an increase in the expected ratio, and (b) the severity of
the increase in the expected ratio. We found that the pigeons were most likely to persist nonoptimally
through the longer expected ratios when stimulus changes were absent and when the increase in
the expected ratio was less severe. Experiment 4 employed a similar procedure with human subjects
that manipulated only the severity of the increase in the expected ratio and found a result similar
to that of the pigeon experiment. In Experiment 5, we tested the hypothesis that a particular history
of reinforcement would induce pigeons to persist through the longer expected ratios; the results
suggested instead that the history of reinforcement caused the pigeons to persist less compared to
pigeons that did not have that history.
Key words: sunk cost, Concorde fallacy, escalation, choice, diminishing returns, discriminative stim-
uli, pigeons
The sunk cost effect is the tendency to per- ioral ecology literature and showed that in ev-
sist in an endeavor once an investment of ef- ery case, behaviors thought to be influenced
fort, time, or money has been made. The ef- by past investment could be explained in
fect is considered maladaptive because only terms of future gains. They suggested that an-
marginal costs and benefits, not past costs, imals might not fall prey to the sunk cost ef-
should factor into rational decision-making. fect because they do not follow rules or
Alternatively called escalation of commitment norms unique to humans, such as ‘‘don’t
or entrapment, this effect has been docu- waste.’’
mented in numerous studies with humans In spite of the lack of evidence for the Con-
(Arkes & Blumer, 1985; Moon, 2001; Staw & corde fallacy, certain lines of research with
Hoang, 1995). Theories accommodating the humans suggest the possibility that nonhu-
effect include self-justification (Staw, 1976), man animals could display this effect. For ex-
prospect theory (Whyte, 1986), and a desire ample, reinforcement history has been shown
to avoid waste (Arkes & Blumer, 1985). to affect suboptimal persistence in an invest-
In nonhuman animals, the effect is called ment (Goltz, 1992, 1993, 1999). Both the par-
the Concorde fallacy. A review by Arkes and tial reinforcement extinction effect (Goltz,
Ayton (1999) concluded that there are no 1992) and behavioral momentum (Goltz,
clear-cut instances of the Concorde fallacy in 1999) have been implicated as mechanisms
nonhumans. They examined purported in- through which reinforcement history could
stances of the Concorde fallacy in the behav- result in persistence.
Second, it often appears that uncertainty is
Research and manuscript preparation were supported at the root of persistence. For example, hu-
by National Institute of Mental Health Grant MH57127.
We thank Dr. Arturo Bouzas of Universidad Nacional Au- man subjects will persist in an unprofitable
tonoma de Mexico for helpful suggestions on the design research and development project in its early
of Experiment 2. stages, but as losses mount subjects de-escalate
Correspondence concerning this article should be ad- commitment (McCain, 1986). Given that
dressed to Anton D. Navarro at the Department of Psy-
chology 0109, University of California, San Diego, 9500
these subjects eventually behave correctly by
Gilman Drive, La Jolla, California 92093-0109 (e-mail: de-escalating commitment, the incorrect per-
anton [email protected]). sistence in the early stages of the project may
1
2 ANTON D. NAVARRO and EDMUND FANTINO
indicate that the subjects do not yet know in in which an investment has been made to-
those early stages that the project is unprof- wards a goal, negative feedback concerning
itable. McCain concluded that escalation and the investment has been received, and the in-
de-escalation are learning processes in which vestor can persist in the investment or aban-
optimal behavior surfaces only when the eco- don it in favor of a new one. In our proce-
nomics of the situation become clear. Bragger dure, pigeons begin a trial by pecking on a
and her associates (Bragger, Bragger, Hantu- key for food. The schedule on the food key
la, & Kirnan, 1998; Bragger, Bragger, Hantu- arranges a course of action with initially good
la, Kirnan, & Kutcher, 2003) explored this hy- prospects that turns unfavorable. On a given
pothesis further in their studies on hysteresis. trial, one of four fixed-ratio (FR) schedules is
Their subjects had to choose whether to con- in effect: short, medium, long, or extra long.
tinue with or abandon hypothetical invest- On half the trials, the short ratio is in effect;
ments while receiving negative economic on a quarter of the trials, the medium ratio
feedback concerning the investments. In one is in effect; and on a quarter of the trials ei-
condition, subjects received unambiguous ther of the two long ratios is in effect. With
feedback—the investment consistently pro- these parameters, after the pigeons have
duced losses of a similar magnitude. In an- emitted the response number required by the
other condition, subjects received ambiguous short ratio, if no reinforcement has occurred
feedback—the investment produced losses of (because one of the longer ratios happens to
var ying magnitude, and occasionally pro- be in effect), then the initially easy endeavor
duced a gain, though the average return was has become more arduous—the expected
equal to that of the former condition. Sub- number of responses to food is now greater
jects with ambiguous feedback persisted in than it had been at the onset of the trial.
the project significantly longer than subjects We gave pigeons the option of escaping the
with unambiguous feedback, and subjects now less favorable endeavor by allowing them
with the opportunity to purchase additional to peck an ‘‘escape’’ key that initiates a new
feedback quit the project significantly sooner trial. If the short ratio does not happen to be
than subjects without that opportunity. To ex- in effect on a given trial, then once the value
plain these results, Bragger and her associates of the short ratio has been met the optimal
cited Bowen’s (1987) equivocality theory of choice is to peck the escape key (and then
escalation. Similar to McCain’s hypothesis, begin anew on the food key). That is, the ex-
equivocality theory posits that decision-mak- pected ratio given escape is lower than the
ers in escalation situations are trying to make expected ratio given persistence. Note that at
sense out of uncertain information. While this choice point the pigeons encounter a
trying to decipher variable feedback on an sunk cost decision scenario. Namely, they
investment, decision-makers may be better off have made an initial investment, they have re-
continuing to invest until it is certain that the ceived negative feedback—no reinforce-
investment is suboptimal. ment—and they can either persist in the ven-
We propose that if uncertainty and rein- ture or abandon it in favor of a better one.
forcement history can influence persistence This general procedure allows us to exam-
in humans, these variables may plausibly ine the role of uncertainty in the sunk cost
bring about persistence in nonhuman ani- effect in two ways. One way is through the
mals. This reasoning forms the basis for our presence or absence of stimulus changes. If a
resent study. stimulus change occurs at the moment when
escape becomes optimal, then the economics
BEHAVIOR-ANALYTIC ANALOG OF of the situation should be more salient than
THE SUNK COST EFFECT if no stimulus change occurs. We hypothe-
In the present study, we set out to explore sized that pigeons responding on this proce-
conditions of uncertainty and reinforcement dure with no stimulus change would persist
history under which pigeons might persist in more than pigeons responding on this pro-
a losing course of action. To this end, we be- cedure with a stimulus change present. A sec-
gan by designing an operant procedure that ond way to manipulate uncertainty is by vary-
models the sunk cost decision scenario. We ing the difference between the expected
define a sunk cost decision scenario as one value of persisting and the expected value of
SUNK COST IN PIGEONS AND HUMANS 3
escaping. The closer these expected values be illuminated with white, red, blue, or green
are to each other, the less salient the advan- light. A minimum force of approximately
tage of escaping and the more likely the pi- 0.15 N was required to operate each key. All
geons should be to persist. chambers had a houselight on the wall 5 cm
This procedure also allows us to examine above the center key for general illumination,
the role of reinforcement history in the sunk and a grain magazine with an opening 5 cm
cost effect. Specifically, how would escape be- by 6 cm centered 14 cm below the center key.
havior change in pigeons that are first trained During magazine operation, the houselight
on this procedure without the escape key? and all keylights turned off and a magazine
These pigeons would have a history of rein- light turned on. The chambers were con-
forcement for persistence on the food key, trolled from an adjacent room by an IBM -
which ultimately leads to food. We hypothe- compatible computer programmed in Turbo
sized that this history of reinforcement would Pascal .
lead to greater persistence when the escape
key is later introduced, compared with pi- Procedure
geons that are placed directly in the escape On every trial, one of four FR schedules
procedure. was in effect on the center (food) key. Com-
Finally, by modifying this procedure for use pletion of an FR schedule resulted in 3 s of
with human subjects, we can extend previous access to grain, followed by a 1-s blackout and
findings with human subjects to a novel for- a new trial. On one half of the trials, the
mat. In particular, we replicate with humans schedule was FR 10; on one fourth of the tri-
one of the pigeon experiments manipulating als, the schedule was FR 40; on one eighth of
economic salience. Our hypothesis is that the trials, the schedule was FR 80; and on one
both pigeon and human subjects should per- eighth of the trials, the schedule was FR 160.
sist more as the salience of economic infor- These schedules were presented randomly.
mation decreases. Throughout every trial the left (escape)
key also was active. One response to this key
produced a 1-s blackout followed by a new
EXPERIMENT 1 trial.
In our first test, we compared persistence We employed a within-subject design in
on the food key when stimulus changes were which we manipulated the presence or ab-
present versus when stimulus changes were sence of stimulus changes. The 4 pigeons first
absent. were placed in this procedure with stimulus
changes present. The stimulus changes sig-
M ETHOD naled a change in the expected value of the
Subjects ratio on the food key. At the start of a trial,
the food key was white and the expected val-
The subjects were 4 naive White Carneau ue was 45 (45 .5∗10 .25∗40 .125∗80
pigeons maintained at about 80% of their .125∗160). After the 10th response, if no re-
free-feeding weights. They were individually inforcement occurred (because one of the
housed and had free access to water and grit. longer ratios happened to be in effect), the
food key turned red, and the expected value
Apparatus
became 70 (70 .5∗30 .25∗70 .25∗150).
Four square operant chambers were used, After the 40th response, if no reinforcement
measuring 37 cm long by 37 cm wide by 37 occurred, the food key turned blue, and the
cm high. All chambers had three keys on one expected value became 80 (80 .5∗40
wall. The left key was 11 cm from the left .5∗120). After the 80th response, if no rein-
edge of the wall, the right key was 11 cm from forcement occurred, the food key turned
the right edge of the wall, and the center key green, and the expected value remained at
was exactly in between. All keys were 25 cm 80.
above the chamber floor and measured 2.5 The pigeons first were trained to peck the
cm in diameter. Only the left and center keys white response key by hand shaping, and
were used. The left key could be illuminated then trained on white, red, blue, and green
with a white ‘‘X,’’ and the center key could stimuli separately with increasingly large FR
4 ANTON D. NAVARRO and EDMUND FANTINO
Table 1 five to eight sessions of the stimulus-changes-
Percentage of trials with persistence in Experiment 1. present condition were lost because of a com-
puter malfunction. The data shown in Table
Pigeon
Session of 1 for this condition are from the first five ses-
stable period 361 362 363 364 sions for which data are available. Behavior in
Stimulus changes presenta this condition already was stable during the
1 0 0 0 0 first five sessions for which data are available.)
2 0 0 0 0 Each datum is the percentage of the trials
3 0 0 0 0 with an opportunity for persistence (FR 40,
4 0 0 0 0 FR 80, and FR 160 trials) that the pigeon
5 0 0 0 0
completed. When stimulus changes were
Stimulus changes absent present, behavior was optimal. That is, the pi-
1 3 100 97 100 geons always escaped during the FR 40, FR
2 4 100 100 100
3 1 100 100 100 80, and FR 160 trials. When stimulus changes
4 1 100 100 100 were absent, the opposite was typically true.
5 2 100 100 100 Three of the 4 birds completed virtually all
Note. Persistence in a trial is defined as completion of of the persistable trials, while only Pigeon 361
that trial (excluding FR 10 trials). retained optimal behavior.
a The data for the first five to eight sessions of this con-
dition were lost because of a computer malfunction. The D ISCUSSION
data shown here are from the first five sessions for which
data are available. For this reason it is unknown for each Experiment 1 represents the first test of
pigeon whether ‘‘Session 1’’ is the first session of the our operant analog of the sunk cost effect.
stable period or is instead subsequent to the first session For many trials, pigeons underwent a course
of the stable period. of action that initially was likely to require few
responses, but half of the time ended up re-
quiring many responses. When the expected
schedules until they responded regularly to ratio increased, the pigeons could either per-
an FR 60. The pigeons received no training sist in the trial or abandon it in favor of a new
on the escape key or the white ‘‘X’’ stimulus. trial with better prospects. When stimulus
After training was completed, the pigeons changes were present that signaled increases
were placed in the procedure one session per in the expected ratio, the pigeons uniformly
day, about 6 days per week, for a total of 30 abandoned the nonoptimal endeavor. When
to 33 sessions. Sessions were terminated after stimulus changes were absent, 3 of the 4 pi-
the delivery of 80 reinforcers. geons nearly always persisted in the endeavor.
In the stimulus-changes-absent condition, These results suggest that stimulus changes
the same 4 pigeons were placed in the above may heighten the salience of changes in the
procedure but without the stimulus changes. schedule of reinforcement. In addition, the
In this condition, the FR schedules and their results are consistent with our hypothesis that
corresponding probabilities were identical to by reducing this salience, pigeons can be in-
those of the former condition, but the center duced to persist in a nonoptimal course of
key remained white throughout each trial. action.
The 4 pigeons were placed in this condition There are two important limitations to Ex-
for 27 sessions. periment 1. One limitation is that Experi-
ment 1 was an AB design, which leaves open
R ESULTS the possibility that factors other than our in-
Nonoptimal persistence was defined as tended manipulation induced the overall
completion of an FR 40, FR 80, or FR 160 change in behavior seen across conditions.
trial. Completion of an FR 10 trial does not Fortunately, the likelihood of this possibility
count as persistence because escape does not is reduced considering that each condition is
become optimal until after the 10th food-key repeated in subsequent experiments in this
response. We visually determined when the paper. The stimulus-changes-present condi-
pigeons’ behavior had become stable. Table tion is repeated with different sets of pigeons
1 displays the data for the first five sessions in Experiments 2 and 5, and the stimulus-
of the stable period. (The data from the first changes-absent condition is repeated in Ex-
SUNK COST IN PIGEONS AND HUMANS 5
periment 3. In each case, the result of the FR 10; on seven twelfths of the trials, the
corresponding condition from the present schedule was FR 30; and on two twelfths of
experiment is replicated. This suggests that the trials, the schedule was FR 50. At the start
the important determinant of the pigeons’ of a trial, the food key was white and the ex-
behavior was our intended manipulation, not pected ratio was 28.3; after the 10th response,
some other factor. if no reinforcement occurred (because one
Another limitation to the present experi- of the longer schedules happened to be in
ment is the following: it has been widely dem- effect), the food key turned red and the ex-
onstrated that pigeons behave ‘‘impulsively’’ pected ratio lowered to 24.4; after the 30th
toward short delays to food (Fantino, 1966; response, if no reinforcement occurred, the
Rachlin, 2000). The fact that pecking the es- food key turned blue and the expected ratio
cape key leads to the possibility of a very short lowered to 20. Thus as the pigeons pro-
FR on the food key may have overridden all gressed through a trial the expected ratio be-
other factors. That is, even if persistence on came shorter.
the food key were the optimal behavior, the Of the 4 pigeons, 2 pigeons first faced the
possibility of a short FR on a new trial still escape-optimal condition and subsequently
may have led the pigeons to escape. Thus the faced the persistence-optimal condition. The
pigeons in the stimulus-changes-present con- other 2 pigeons faced these conditions in re-
dition may have tended to escape not because verse order. The pigeons were placed in each
they were sensitive to the true reinforcement condition for 29 sessions.
contingencies, but because they behave im-
pulsively toward short delays to food. R ESULTS
We addressed this possibility in Experiment Persistence was defined as the completion
2 by retaining the stimulus changes and the of any ratio that was not the short ratio.
short FR and by comparing behavior when Hence, in both conditions, the trials with op-
escape is optimal, as in Experiment 1, with portunity for persistence were all trials except
behavior when persistence is optimal. for the FR 10 trials. Table 2 displays the per-
centage of the trials with opportunity for per-
sistence that each pigeon completed. For
EXPERIMENT 2 each condition, data are taken from the first
M ETHOD five sessions of the period of stable behavior.
In the escape-optimal condition, 3 of the 4
Subjects pigeons persisted on 0% of the trials through-
The subjects were 4 White Carneau pi- out this period; the other pigeon (W524) per-
geons with previous experience with unrelat- sisted on roughly one fourth of the trials. In
ed procedures. They were maintained at the persistence-optimal condition, 3 of the 4
about 80% of their free-feeding weights, were pigeons persisted on nearly 100% of the trials
individually housed, and had free access to during the stable period, and the other
water and grit. (W524) typically persisted on 80% to 85% of
the trials during this period.
Apparatus
Same as for Experiment 1. D ISCUSSION
Experiment 2 served two functions. First, it
Procedure provided a replication of the stimulus-chang-
In a within-subject design, the pigeons es-present condition of Experiment 1. In Ex-
faced two conditions: escape-optimal and per- periments 1 and 2, pigeons correctly aban-
sistence-optimal. The escape-optimal condi- doned a course of action that had turned for
tion was identical to the stimulus-changes- the worse when stimulus changes were pres-
present condition of Experiment 1. ent that signaled the downturn. Second, Ex-
In the persistence-optimal condition, the periment 2 addressed the possibility that the
FR schedules and their corresponding prob- results of the stimulus-changes-present con-
abilities were arranged such that persistence dition of Experiment 1 could be explained in
was the optimal behavior. On three twelfths terms of impulsivity. In Experiment 1, be-
of the trials, the schedule on the food key was cause responding to the escape key produced
6 ANTON D. NAVARRO and EDMUND FANTINO
Table 2
Percentage of trials with persistence in Experiment 2.
Pigeon
Session of
Condition stable period W501 G354 W524 W520
Escape optimal 1 0 0 26 0
2 0 0 16 0
3 0 0 14 0
4 0 0 54 0
5 0 0 5 0
Persistence optimal 1 100 100 83 98
2 100 100 83 100
3 100 100 85 100
4 100 100 82 94
5 100 100 81 98
Note. Persistence in a trial is defined as completion of that trial (excluding FR 10 trials).
the possibility of a very short FR schedule on mal. We found that pigeons indeed behaved
the food key, pigeons in the stimulus-changes- optimally when stimulus changes were pres-
present condition may have responded to the ent, whether optimal behavior meant persist-
escape key not because it was optimal, but ing or escaping. By withholding stimulus
because they behave impulsively towards changes in Experiment 1, we induced 3 of the
short delays to food. We tested this possibility 4 pigeons to persist in a losing course of ac-
by keeping the short FR in Experiment 2 but tion.
making persistence optimal. If responses to
the escape key in Experiment 1 were caused
by impulsivity, then the pigeons in Experi- EXPERIMENT 3
ment 2 also should have responded to the
In Experiment 3, we examined a second
escape key even though persistence was op-
way of manipulating economic salience—ma-
timal. We found instead that the pigeons
tended to behave optimally whether escape nipulating the difference between the ex-
or persistence was optimal. pected ratio given escape and the expected
We do note that the FR 10 in the persis- ratio given persistence. We repeated the stim-
tence-optimal condition of Experiment 2 had ulus-changes-absent condition of Experiment
a relatively low probability of occurrence (p 1 but with three different sets of FR schedules
.25) compared with the FR 10 in the es- that narrowed or widened the mathematical
cape-optimal condition (p .5). Because of difference in the expected value of persisting
this difference, the persistence-optimal con- versus escaping. When these two values are
dition may have been less likely to generate more similar, the optimal choice should be
impulsivity towards the FR 10. This may pro- less obvious. We hypothesized that the pi-
vide an alternative explanation for the rela- geons would be more likely to persist when
tive absence of escape responses in the per- these two values were more similar.
sistence-optimal condition. Nevertheless, our
M ETHOD
results are consistent with the hypothesis that
behavior was dictated by optimality, not im- Subjects
pulsivity.
Experiments 1 and 2 examine one way of The subjects were the 4 White Carneau pi-
manipulating economic uncertainty in a sunk geons used in Experiment 1. They were main-
cost situation: presenting or withholding tained at about 80% of their free-feeding
stimulus changes that signal when a course of weights, were individually housed, and had
action has changed value. We hypothesized free access to water and grit.
that when stimulus changes are present, the Apparatus
economics of a situation should be more sa-
lient and behavior should tend toward opti- Same as for Experiments 1 and 2.
SUNK COST IN PIGEONS AND HUMANS 7
Table 3
Expected ratios as a trial progresses, Experiment 3.
Stage at which expected ratio takes effect
(if no reinforcement occurs)
After response After response After response
Start of number required number required number required Difference between
Condition trial by short FR by medium FR by long FR persisting and escapinga
5, 50, 100, 55 100 110 120 100 (55 1) 44
220
10, 40, 80, 45 70 80 80 70 (45 1) 34
160
20, 50, 100, 60 80 100 100 80 (60 1) 19
200
a See text for explanation.
Procedure that did not have the short FR (in the 20, 50,
In all conditions, the food key remained 100, 200 condition, this was all but the FR 20
white throughout every trial. Three different trials; in the 10, 40, 80, 160 condition, this
sets of FR schedules were used in a within- was all but the FR 10 trials; in the 5, 50, 100,
subject design: 5, 50, 100, 220; 10, 40, 80, 160; 220 condition, this was all but the FR 5 trials).
and 20, 50, 100, 200. The corresponding Table 4 displays the percentage of the trials
probabilities of the short, medium, long, and with opportunity for persistence that each pi-
extra-long ratios were equal to those used in geon completed. For each condition, the data
Experiment 1; thus the 10, 40, 80, 160 con- are taken from the first five sessions of the
dition was a replication of the stimulus-chang- period of stable behavior. In the 5, 50, 100,
es-absent condition of Experiment 1. Table 3 220 condition, the percentage of trials with
displays the sequence of the expected ratios persistence was at or near zero for all 4 pi-
in each condition. The critical factor distin- geons. In the 10, 40, 80, 160 condition, the
guishing the conditions is the mathematical percentage of trials with persistence was near
difference between the expected ratio given zero for Pigeon 361, but at or near 100 for
escape (i.e., one response to the escape key Pigeons 362, 363, and 364. In the 20, 50, 100,
plus the expected ratio at the start of a trial) 200 condition, the percentage of trials with
and the expected ratio given persistence (i.e., persistence was at or near 100 for all 4 pi-
the expected ratio after the response number geons.
required by the short FR has been completed,
if no reinforcement has occurred). In the 5, D ISCUSSION
50, 100, 220 condition, the mathematical dif- The present experiment served two func-
ference is 44. That is, escaping as soon as it tions. First, the 10, 40, 80, 160 condition of
becomes optimal will lead to food on average this experiment replicated the findings from
in 44 fewer responses than persisting. In the the stimulus-changes-absent condition of Ex-
10, 40, 80, 160 condition, the difference is 34. periment 1. Second, the present experiment
In the 20, 50, 100, 200 condition, the differ-
tested the hypothesized role of economic sa-
ence is only 19. Thus the advantage of escap-
lience in persistence by exploring a variable
ing had a different salience in each condi-
tion. not manipulated in Experiments 1 and 2: The
The order of conditions was 20, 50, 100, size of the mathematical difference between
200; 10, 40, 80, 160; and 5, 50, 100, 220. The the expected ratio given escape and the ex-
first condition lasted 26 sessions; the second pected ratio given persistence. As hypothe-
condition lasted 35 sessions; the third condi- sized, when this mathematical difference was
tion lasted 20 sessions. larger the pigeons typically behaved optimally
by abandoning the nonoptimal trials. When
R ESULTS this mathematical difference was smaller, the
As in Experiments 1 and 2, the trials with pigeons did not behave optimally, but rather
opportunity for persistence were the trials tended to persist in nonoptimal trials. To-
8 ANTON D. NAVARRO and EDMUND FANTINO
Table 4
Percentage of trials with persistence in Experiment 3.
Pigeon
Session
Condition stable period 361 362 363 364
5, 50, 100, 220 1 13 9 0 0
2 4 15 0 0
3 16 8 0 3
4 9 8 0 0
5 7 3 0 0
10, 40, 80, 160 1 0 90 100 100
2 22 100 100 100
3 19 89 96 100
4 19 100 94 100
5 1 100 100 100
20, 50, 100, 200 1 93 100 100 100
2 91 100 100 95
3 93 97 91 100
4 100 100 98 100
5 90 100 95 100
Note. Persistence in a trial is defined as completion of that trial (in the 5, 50, 100, 220 condition, excluding FR 5
trials; in the 10, 40, 80, 160 condition, excluding FR 10 trials; in the 20, 50, 100, 200 condition, excluding FR 20
trials).
gether with


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