Spinning Works: Strategy Framing in the One-Shot Prisoner’s Dilemma Game
Rob Moir (UNB Saint John)
Abstract:
The one-shot prisoner’s dilemma game has a unique dominance-solvable equilibrium. While
others have studied framing some aspects of the game under laboratory conditions, the effects of
non-neutral strategy labels has received significantly less study. In this experiment, I compare
the effects of non-neutral strategy labels to baseline conditions, under both complete and
incomplete information conditions. Strategy labels influence how subjects act in a one-shot
prisoner’s dilemma environment. While information condition seems to play little role in
subject’s decisions, it seems to affect their ex post predictions of others’ behaviour.
Key words:
prisoner’s dilemma, one-shot, framing, experiment
JEL:
C72, C91
This Version: June 2011
PRELIMINARY DRAFT – PLEASE DO NOT QUOTE WITHOUT AUTHOR’S
PERMISSION
Strategy Framing in the One-Shot Prisoner’s Dilemma Game
1. Introduction
What influences cooperative behaviour in humans? The answer to this question is important to
economists as it affects our descriptive models and consequently our prescriptive
recommendations. Indeed, from a policy perspective cooperation can be both welfare improving
(provision of public goods, management of a common-pool resource) and welfare decreasing
(collusion, price-fixing).
While traditional economic incentives like prices and taxes have long been known to affect
economic behaviour (e.g., Pigou, 1920), the possibility of framing effects on human behaviour is
a relative newcomer to the field (Schelling, 1960; Kahneman and Tversky, 1984). While the
framing literature is rich, the role of framing through strategy labels is surprisingly sparse. In
this paper, I explore how strategy labels affect cooperation in a one-shot prisoner’s dilemma
(PD) game under both complete and incomplete information. These results are unique in that
truly one-shot PD experiments are rare, as is the study of information in PD games. Moreover, a
novel labelling treatment in which traditionally framed strategy labels are reversed permits
further analysis of how labels might influence decisions and predictions in this environment.
The remainder of this paper is organized in the following manner. Section 2 contains a literature
review of both the PD game and experimental analysis of framing effects. In Section 3, the
experiment and hypotheses are outlined. Section 4 presents the results and discussion while
Section 5 concludes.
2. Literature Review
Game theory is an important tool used to analyze interaction between self-determining agents.
Arguably the most famous game within academe is the PD. It has been used in Policy Studies,
Economics, Political Science, Sociology, Psychology, Sports Studies, Business, Maths, and
Biology, in part because it captures the essence of a broader class of games known as social
dilemmas (Dawes, 1980).1 Between 1960 and 2010, there have been approximately 2,000
independent peer-reviewed articles discussing the PD.2
1
Dawes claims all social dilemmas share two properties: (1) an individual receives a higher payoff for a “socially
defecting” choice as compared to a “socially cooperative” choice regardless of the decisions of others, and (2)
everyone involved is better-off if all cooperate than if all defect.
2
Searching multiple academic databases (EconLit, Academic Search Premier, Business Source Premier, Criminal
Justice Abstracts, International Security & Counter Terrorism Reference Center, PsycARTICLES, PsycINFO,
Wildlife & Ecology Studies Worldwide) and accounting for multiple occurrences across databases, there were 1,997
independent published peer-reviewed articles between 1960 and 2011, 955 of which have been published since 2000
(search conducted 5 November 2010). The keyword search term used was “prisoner* dilemma*” (to allow for
1
According to historical record, a game with a PD-like structure was first produced by Merrill
Flood and Melvin Dresher in January 1950 (Flood, 1952) while they worked for the U.S. Air
Force’s RAND Corporation (Kuhn, 2009). RAND was interested in game theory’s possible
“applications to global nuclear strategy” (Kuhn). Published in 1952, the original game was
asymmetric, involved losses and gains, and was markedly unframed (Flood, 1952: pp.17-24a).3
Albert Tucker recalls seeing this game in Dresher’s office at RAND (Straffin, 1980). Asked to
present a lecture on game theory to Stanford psychologists, Tucker recast the game in its
symmetric form, told a story about two suspects arrested for a joint crime, applied strategy labels
of “confess” and “not confess” to strategies, and renamed the game “a two-person dilemma”
(Tucker, 1950). The leap to “prisoner’s dilemma” is a natural extension to, and simple shorthand
for, this story and provided the first frame for this particular game.
A typical version of the PD game is presented in Figure 1 below.
Figure 1 A Generic PD Game {about here}
The standard theoretical solution to this game, assuming it is played once between anonymous
non-communicating players making simultaneous decisions, is for the row player to choose
strategy {Down} and the column player to choose strategy {Right}. Adopting strategy {Down}
({Right}) is a dominant strategy – a strategy leading to the highest outcome possible regardless
of the choice of the other player – for the row (column) player. Moreover, adopting strategy
{Down} ({Right}) is a maximin strategy – a strategy ensuring the highest worst-possible
outcome for a player – for the row (column) player. Both methods of strategic reasoning are
unaffected by knowledge of the other player’s payoffs (so information condition does not
matter), or the particular labels attached to Up, Down, Left, or Right.4
various apostrophe and pluralisation combinations). Specifically including the various combinations and using the
Boolean OR operator, the number increases to 2,006 articles between 1960 and 2011.
3
Flood also conducted the first experiment using the game. Subjects identified as AA and JW made simultaneous
decisions with feedback for 100 trials and paid them according to their decisions. Subject diaries kept during the
experiment clearly indicate that subjects themselves framed the game. For instance, JW comments he was trying to
entice AA to a “mutually profitable” outcome. JW further comments, “[AA is] a shady character and doesn’t
realize we are playing a 3rd party, not each other” (Flood, 1952: pp. 41-42). JW also describes an endgame move to
switch strategies as “conservative” (Flood, 1952: p. 41). Despite the frameless environment, players naturally apply
values to actions and consequently develop a frame in which they contextualize the game.
4
The assumption of a one-shot simultaneous choice game is critical to these theoretical predictions. Nash noted that
in the Flood and Dresher experiment, repetition of choices between the same players meant that the entire session
should be considered as “one large multimove game” with an additional grim-trigger strategy that leads players to
the Pareto-superior equilibrium (Flood, 1952: pp. 24-24a). In order to have the cleanest predictions possible, the
current experiment has anonymous participants make a single simultaneous decision in a PD game followed by an
ex post prediction of what strategy some other subject had chosen. Many of the related experiments discussed in this
section use data from iterated prisoner’s dilemma (IPD) games or involve a series of different games.
2
While researchers conducting PD experiments have “steadfastly removed all labels from
participants’ view, value labels are regularly used to interpret subject behaviour” (Zhong et al.,
2007: p. 433).5 Indeed, it is the immutability of the dominant solution to context that permits us
as instructors to teach the PD game once and apply it to such diverse topics as confession
extraction, price wars, collapse of the fisheries, advertising wars, duopoly production decisions
and nuclear defence.
The explicit study of framing arguably began with Schelling’s work on focal points (1960) and
Kahneman and Tversky’s work on decision-making under uncertainty in the early 1980’s (see
Kahneman and Tversky, 1984 for a summative overview of this literature). Forgiving a certain
amount of overlap, framing research can be broken down into two broad areas: valence framing
in which information is presented in a positive or negative frame (e.g., giving to the public fund
versus taking from the public fund, gains versus losses) and pure framing in which different
words are used to title the scenario but the game is otherwise objectively the same (e.g.,
psychological priming, naming the game, strategy and outcome labels) (Elliott and Hayward,
1998).
Social dilemma experiments testing for valence framing effects typically compare a “giving”
frame as in contributions to a public good to a “taking” frame as in depletion of a common-pool
resource (Dawes, McTavish, and Shaklee, 1977; Brewer and Kramer, 1986; Fleishman, 1988;
Andreoni, 1995; de Heus et al., 2010). Results are mixed. Other experiments compare behaviour
in functionally equivalent games (e.g., a sequential social dilemma versus an ultimatum game in
Larrick and Blount, 1997). Valence frames, however, are not the focus of this experiment.
Pure framing effects do not change the rules or the payoffs of the game but alter the context
within which it is played. While Flood and Dresher’s game was presented in a neutral
framework – the game was simply titled “a game” and strategies were labelled {1} and {2} –
Tucker’s contextualization as a police interrogation tactic with strategies of {not confess}
(replacing {Up} and {Left} in Figure 1) and {confess} (replacing {Down} and {Right}) might
change behaviour without altering payoffs.6 Further behavioural changes may take place if, as
might be viewed by co-conspirators, {not confess} is replaced by {be strong} and {confess} is
replaced by {snitch}.
The above framing scenarios might reflect internal contextualization of the situation by either
officers or the suspects. Suppose that the framing was more deliberate. Recall that PD game was
5
Murnighan and Roth (1983) and de Heus, Hoogervorst, and van Dijk (2010) are two examples of research papers
introducing the PD with the strategy labels cooperate/defect, ensuring that subjects did not see such labels, and
subsequently discussing the resulting behaviour in terms of value labels.
6
In these instances, one should think of payoffs as subjective utility values with higher values reflecting greater
utility.
3
formulated in order to explore emerging realities in a world with nuclear weaponry (Kuhn,
2009). An explanation for the nuclear arms race might be created if one replaces {not confess}
with {not build} and {confess} with {build}. Rational agents would independently choose
{build} resulting in a world so-much-the-poorer for engaging in an arms race. This theoretical
equilibrium may not be realized if agents get additional (extra-model) utility from not building.
Is it possible to frame the situation to make this extra-model utility from not building smaller,
perhaps even disappear, or even make amassing weapons a socially positive action?
The “nuclear arms race” could be relabelled as “security through mutually assured destruction.”
A strategy of {not build} might become {risk nuclear war} and {build} replaced with {ensure
stability}. It is easy to see how Orwellian doublespeak (Lutz, 2000) in both the framing of the
situation and the strategies might reinforce the selection of the dominant strategy, and in this case
lead to nations amassing a massive nuclear arsenal.7 Indeed, the concept of mutually assured
destruction was developed with game theory and rational choice in mind and an equilibrium that
met a very certain policy objective of nuclear arsenal expansion (Chwastiak, 2001: pp. 512-513).
Today we might recognize this as “spinning” a story.
A number of experiments show that explicitly naming the game (e.g., the Wall Street Game
versus the Community Game) or priming subjects through word association or the reading of
news briefs can significantly alter subject behaviour in PD (Eiser and Bhavnani, 1974; Batson
and Moran, 1999; Kay and Ross, 2003; Liberman, Samuels, and Ross, 2004; Ellingsen,
Johannesson, Munkhammar, and Möllerström, 2009) and linear public good games (Elliott,
Hayward, and Canon, 1998; Rege and Telle, 2004).8 There is just one experiment that considers
both valence and pure framing effects. Dufwenberg, Gächter, and Hennig-Schmidt use a oneshot linear public good experiment interacting both the valence frame (“give” versus “take”) and
the pure frame (neutral versus “community” label) and conclude that “frames influence beliefs
and beliefs influence behavior” (2010: p. 31).
Strategy labelling is an example of pure framing. Only four studies exist that use explicit
strategy labels such as cooperate and compete/defect in the experiment (Oskamp and Perlman,
1965; Johnston, Markey, and Messe, 1973; Rilling et al., 2002; Zhong, Lowenstein, and
7
“Doublespeak” does not appear in George Orwell’s dystopian novel, Nineteen Eighty-Four first published in 1949.
It is an amalgam of “doublethink” and “newspeak.” The word “doublespeak” fits into the definition of B vocabulary
within Newspeak – “words which had been deliberately constructed for political purposes: words, that is to say,
which not only had in every case a political implication, but were intended to impose a desirable mental attitude
upon the person using them” (Orwell, 1981: p. 302) – as does the phrase “mutually assured destruction.”
8
In a linear public good experiment, the dominant solution is for subjects to free-ride (contribute nothing). The
Pareto optimal solution is for each subject to contribute 100% of their resources to the public good. In the public
good environment, there are a number of non-dominant strategies available to each player and generally more than
two players. In the PD game, there are only two strategies, one of which is dominant, and typically involve only two
players.
4
Murnighan, 2007) but in Rilling et al. the labels are used to present the game to subjects but are
not themselves systematically studied. The remaining three studies all used fixed-pair iterated
PD games as the data generating process and analysed data as if it were independent. As Nash
notes, the equilibrium strategy in a repeated PD game with fixed partners is not necessarily the
same as that in a one-shot game (Flood, 1952: pp. 24-24a) and certainly cannot be analyzed as if
it is independent. Moreover, two of the experiments, Johnston et al. and Zhong et al.,
misrepresent the “partner” to the subjects, claiming that it is a real person when it is in fact a
predetermined strategy: a reluctant and forgiving trigger in the former and a variant upon tit-fortat in the latter.9 Strategy labels are found to have negligible effects (Oskamp and Perlman) or
marginal interactive effects with female subjects enhancing non-dominant behaviour (Johnston et
al.). Zhong et al. find strategy labels increase non-dominant behaviour, but draw this conclusion
without appealing to the data from game 1of their sessions which could be considered to be
independent.10 The strongest effects occurred when the word “cooperate” and a variant of its
opposite are used as strategy labels.
3. Experiment Design
3.1 Design
In this experiment, subjects are required to make a one-shot decision in the PD game described
in Figures 2 and 3 below in which outcomes represent dollars to subjects. These figures include
generic strategy labels which are varied according to label treatment (see Table 1). Other than
the strategy labels, these figures are faithful representations of what subjects see in both the
complete information (Figure 2) and incomplete information (Figure 3) treatments.
Capitalization and boldface are used to ensure subjects clearly understand their role in the
experiment.11
Figure 2 A Generic Complete Information PD Game {about here}
Figure 3 A Generic Incomplete Information PD Game12 {about here}
9
In fact, a large number of framing experiments using a PD framework misrepresent to subjects the nature of the
other player.
10
Using these truly independent data the authors find no significant strategy labelling effect beyond the label
treatments applied to the name of the game or the resulting outcome.
11
Subjects are presented a game figure as per Figures 2 and 3. Here I have changed the font of the strategy labels to
ease exposition.
12
In the case of a Row Player with incomplete information the game figure would look like Figure 2 and column
entries would have “?” where numbers currently appear.
5
Because all games are symmetric and decisions are made simultaneously and anonymously, row
and column players are interchangeable. With 100 subjects, the following design table is
established.
Table 1 Experimental Design Table {about here}
Treatments NO and PO are constructed rather than conducted. Conducting ½-Orwellian
treatments, namely OR and OC, means that exactly half the subjects face normal value labels
when they make decisions (NO: column players from OR and row players from OC) while the
other half face Orwellian value labels when they make decisions (PO: row players from OR and
column players from OC), and each sees the opposite strategy labelling to their own in the place
of other’s strategies.
After all decisions in the PD are submitted, subjects are presented with a questionnaire asking for
demographic information. The questionnaire also presents subjects with an identical copy of the
game figure and asks them to predict the choice of their as-yet-unassigned counterpart using the
strategy labels as faced by the counterpart. A correct prediction is worth $1 while an incorrect
prediction earns zero.13
3.2 Hypotheses
Assuming players are rational self-interested money-maximizers, the unique Nash equilibrium
strategy profile for the one-shot PD game for the row and column players respectively is
{R2,C2}. Because the game is symmetric, all players can be cast as a single player (arbitrarily
set to row), leading to a predicted strategy profile of {R2}. This is invariant to strategy labels and
information conditions. The traditional game theoretic hypothesis follows.
Hypothesis One: Subjects always adopt the {R2} strategy.
While theory predicts subjects will use the dominant (or maximin) strategy exclusively,
behavioural results suggests that some subjects will adopt the {R1} strategy even in the absence
of a frame created through strategy labels (i.e., in the NV treatment). If subjects use strategy
labels in addition to payoffs to frame their decisions, then strategy labels will cause them to
deviate from their behaviour in the NV treatment. Traditional strategy labels (e.g.,
R1=“cooperate” and R2=“cheat”), applicable to the V and NO treatments, might cause a subject
to choose {R1}. On the other hand, Orwellian strategy labels (e.g., R1=“cheat” and
R2=“cooperate”), applicable to the PO and OV treatments, might lead subjects to choose {R2}.
13
A sample questionnaire is included in the appendix. It should be noted that subjects’ predictions are solicited after
their decisions are made. Thus, if a subject does not normally predict the action of another before making her
decision, then her standard behaviour in this environment is unaltered.
6
Dominant and maximin strategies require no concept of “other” in order to be enacted. Under
either strategy, a player should play {R2} irrespective of her thoughts about the strategy of an
anonymous other. Thus, there should be no specific pattern to subjects’ predictions because
predictions do not matter in this environment.
Hypothesis Two: Subjects’ predictions are invariant to treatment.
Under incomplete information, subjects do not know the payoffs accruing to the other individual.
No matter the particular strategy a subject chooses, she receives a higher potential payoff if she
ex post predicts the other player to have chosen strategy {R1}. Predicting {R1} on the part of
the other player ex post will make a subject feel better about the decision she has already made.
3.3 Procedure
In each of three sessions, an even number of subjects were seated in a classroom and presented
with a folder labelled only with subject ID.14 Instructions were presented to the participants as a
group. Special attention was paid to teaching subjects how to indicate their decision in a 2x2
normal form game and how a randomly-paired individual’s decision was to be used to determine
payoffs.15,16 Subjects were informed that their decisions were anonymous to both the partner in
the random pairing and to the experimenter – subjects’ decisions were absolutely private.
After instructions were read and any questions answered, subjects were asked to sign an
informed consent form and to indicate their subject number beside their name on a payoff claim
sheet.17 The informed consent sheet was collected by the experimenter while the payoff claim
sheet was collected by a disinterested third party who would pay subjects in the absence of the
experimenter.
Subjects then removed a decision sheet which summarized the instructions and presented them
with a game figure according to the treatment (see Figures 2 and 3 as examples) and indicated
their decision. After their decisions were collected, they were asked to complete a short
14
In the first session, 40 subjects were recruited from the general student population at the University of New
Brunswick in Saint John. The remaining two sessions occurred in a statistics and a writing class with 36 and 24
subjects respectively. While the instructors knew of my arrival, students were unaware of the nature of the
experiment and were told only that there was going to be a visitor.
15
Instructions were presented using PowerPoint or equivalent overheads depending upon available facilities. These
are available upon request from the author.
16
The demonstration game was asymmetric and did not have the pattern of a PD game. Subjects were clearly told
that payoffs in the example were hypothetical.
17
The informed consent sheet was kept by the experimenter. While it has a subject’s name, it contains no
identifying information relative to a session or treatment so it could not be used to identify a subject’s decision.
7
questionnaire. As part of the questionnaire they were again presented with the game figure
identical to the one they had just seen and asked to predict the decision of the random person
they would be paired with (using the other person’s strategy labels); if correct, they would earn
an extra dollar.
Upon completion, subject folders were collected, random pairings between row and column
players within treatment were made, and payoffs determined. Payoffs were placed into
individual envelopes identified by subject ID and returned to the third party for distribution.
Subjects signed at the appropriate play on the payoff claim form which was then placed into a
large envelope, sealed, and submitted to the financial office. At no point could the experimenter
determine the actions of a particular individual and subjects knew this.18
4. Results
A total of 100 subjects participated in this experiment. Sessions lasted approximately 15 minutes
with average earnings of $4.23 (s.d. $2.31) when prediction bonuses are included.19 Summary
data is presented in Table 2 below.
Table 2 Summary Data by Information Condition {about here}
In total, 37% of the subjects in this one-shot PD experiment selected the non-dominant {R1}
strategy. There was little difference in decisions across information conditions. On the other
hand, the information condition seemed to play a bigger role in subjects’ ex post predictions.
Incomplete information means subjects do not have any information on the other player’s
payoffs and must consequently rely upon gut instinct, wishful thinking, inference, or label cues.
In the complete information case subjects could also rely upon payoff cues. This might be
complicated in the Orwellian cases where actions leading to joint payoff maximization are
labelled as “cheating.” The possibility for confusion in labelling is evident when one considers
individuals who project “self” onto “other” and make predictions that are comparable to their
own (see Prediction = Decision entries in Table 2). These differences are quite large when one
considers choices based on outcomes (irrespective of labels) versus choices based on labels.
While not a specific treatment variable, there is no statistical evidence of a particular sex effect
upon strategy selection or predictions.
18
The idea here was to implement a double-blind procedure within the confines of institutional rules on financial
record keeping.
19
At the time of these sessions, the minimum wage was under $10 while the experiment had the equivalent average
hourly payoff of $17. Payoffs ranged from $1 to $8 (or $4 to $32 per hour). Compare this to Zhong et al. (2007)
who had a payoff range of $14 to $16 for 45 minutes work ($18.70 to $21.30 per hour) for a related experiment.
Under their design, the potential gains and losses from cooperation were relatively small.
8
While one might rationalize that if another adopts a strategy {R1} joint payoffs are maximized
by adopting {R1} oneself, it is hard to rationalize adopting an {R1} strategy if one predicts that
another will adopt an {R2} strategy. Perhaps some people believe in “doing what is right” even
though they believe others may not follow this maxim. It is clear in Table 2, instances of
predictions that can be considered as non-rationalizable with respect to decisions are relatively
rare (15% of all observations) and do not systematically vary across information conditions or
labelling treatment. On average, subjects were correct in their predictions 49% of the time. This
result too is invariant to both information condition and strategy labelling.
4.1 Result One
Subjects do not universally adopt the dominant strategy in a one- shot PD game. Furthermore,
labelling one strategy as “cooperate” and another as “cheat” in a PD environment shifts
subjects’ decisions toward the strategy labelled “cooperate.” The effect is most pronounced
when the “cooperate” label corresponds to the dominant strategy (i.e., when Orwellian strategy
labels are used).
We can reject the null hypothesis that subjects always adopt the dominant {R2} strategy as 37%
of all decisions in this one-shot environment were the {R1} strategy. Moreover, as Figures 4
through 6 and the logistic regression results in Table 3 suggest, while information condition does
not have a significant effect on strategy selection, strategy labelling does.
Figure 4 presents the raw data of subjects’ selection of the non-dominant strategy {R1} from
treatments as conducted. Visual inspection confirms that there seems to be a small positive
effect toward selecting the non-dominant strategy {R1} when moving from neutral labels (NV)
to valued labels (V) and a negative effect of moving to Orwellian values (OV). Mixed labelling
conditions (OR and OC), in which only half the subjects had Orwellian labels while the other
half had traditional labels, exhibit little difference from each other and the NV case.
Figure 4 Non-Dominant Decisions by Treatment {about here}
Result one is further supported by regression (1) in Table 3 which contains the results of a
logistic regression of dominant strategy selection {R2} upon labelling and information treatment
conditions.20 Valued labels (V) lead to a lower likelihood of selecting {R2} – and consequently
20
In all instances of regressions in Table 3, a likelihood ratio test for nested models permits dropping the dummy
variable for male subjects. While information condition could be dropped using the same criteria, it is an explicit
treatment variable and has thus been retained. In the PO observations, all 10 subjects’ decisions were for strategy
{R2} in the incomplete information treatment and 9 of 10 decisions were for strategy {R2} in the complete
information treatment. This is comparable to the OV treatment in which 8 of 10 and 9 of 10 decisions were for
strategy {R2} in the incomplete and complete information cases respectively. The perfect prediction of the PO data
in the incomplete information case prevents the construction of a meaningful regression with full interaction
between strategy labels and information condition. The strong similarity in the PO and OV data suggests that the
9
a greater likelihood of selecting {R1} – though not significantly, while Orwellian values
significantly increase the likelihood of selecting {R2}. Estimates of the effects of mixed labels
(OR and OC) show no significant effects as compared to the neutral label (NV) treatment.
Table 3 Logistic Regression: Decision upon Treatments (Standard Errors) {about here}
It is important to recall however, that half of the subjects in the OR and OC treatments had
normal labels (NO) and half played using Orwellian labels (PO). It is quite possible that
subjects in these roles played differently from each other. Figure 5 and regression (2) in Table 3
result from this relabelling.
Figure 5 Non-Dominant Decisions by Treatment (Relabelled Data) {about here}
It is clear that there is a significant change in how data is interpreted after it is relabelled. Now
NO subjects’ decisions closely resemble those of made in the valued strategy labels treatment
(V) – subjects in the mixed environment with normal value labels selected {R1} more often –
and PO subjects’ decisions closely resemble those made in the Orwellian value treatments (OV)
– subjects in the mixed environment with Orwellian labels selected {R2} more often. This
visual evidence is reinforced by the logistic regression results in Table 3 regression (2). The
estimates on the V and NO variables, while not significant, suggest that in those treatments,
subjects were less likely to select the {R2} strategy when compared to subjects facing neutral
labels. Conversely, subjects in the PO and OV treatments were significantly more likely to
select the {R2} strategy as compared to those facing neutral labels.
Pairwise comparisons of regression estimates for labelling treatments reject the null of equality
between estimates for all but V=NO and PO=OV. In other words, subjects facing normal labels
behaved similarly and subjects facing Orwellian labels behaved similarly but the two groups
behaved differently from each other. Collapsing these treatments into a valued treatment
(Valued) and Orwellian (OValued) results in Figure 6 and Table 3 regression (3). Data in
Figure 6 is presented as the percentage of subjects adopting an {R1} strategy.21 The results in
Table 3 regression (3) suggests that facing normal strategy labels increases the likelihood of
adopting an {R1} strategy (this effect is borderline significant with a p-value of 0.101) while
facing Orwellian labels significantly increases the likelihood of adopting an {R2} strategy (pvalue of 0.01).
Figure 6 Non-Dominant Decisions by Grouped Treatment {about here}
strategy labelling treatment matters most and it is safe to drop interactive terms. A likelihood ratio test for nested
models using just NV, V, and OV data confirms that interactive terms can safely be dropped.
21
The original 5x2 experiment design with 10 observations per cell has effectively been reduced to a 3x2 design
with 20 observations per cell in the lower 4 cells.
10
Recent theoretical and behavioural research suggests that there may be personality reasons for
people to cooperate in a one-shot PD environment (Simpson, 2004; Janssen, 2008; Swope et al.,
2008; Wolpert et al., 2010). Simpson in particular argues that while the PD contains both a
“greed component” (the temptation to capitalize on another’s cooperation)22 and a “fear
component” (the fear of being suckered when one is trying to cooperate), prosocial individuals
“routinely transform PD into an “Assurance” Dilemma (AD)” (pp. 386-387). An example of
such a transformation is depicted in Figure 7 below in which outcomes are now a combination of
payoffs and utility.
Figure 7 A Generic Transformed PD AD Game {about here}
This transformed game has two Nash equilibria: {R2,C2} as before and the Pareto superior
{R1,C1}.
One might therefore expect that at least some people with a prosocial disposition will deviate
from the dominant strategy profile {R2} and adopt the Pareto-improving strategy {R1} if they
believe they might be matched with another prosocial individual. Indeed, out of 127 subjects
evaluated, Simpson found 59 were prosocial, and of these 59, 37 adopted a cooperative strategy
in a one-shot PD.23
Simpson observed approximately 48% of all subjects behaving cooperatively in a one-shot PD.
In the current experiment, of the 20 subjects participating in the NV treatment – the treatment
most comparable to Simpson – 8 (40%) adopt the potentially Pareto-improving {R1} strategy.
The regressions in Table 3 suggest that normal strategy labels increase the likelihood of subjects
selecting the {R1} strategy beyond that already existing in a neutral environment whereas
Orwellian strategy labels increase the likelihood of subjects selecting {R2} as compared to the
neutral label environment.
4.2 Result Two
There is little statistical evidence of a strategy-labelling effect upon ex post predictions. There is
some evidence that subjects ex post predict a greater amount of non-dominant strategy choices
on the part of another player under incomplete information. Anecdotal evidence suggests that
there may indeed be strategy labelling, information, and interactive effects, but more data is
needed to draw specific conclusions.
22
Italics here reflect the potential for implicit framing brought to bear by individuals participating in the PD. The
Simpson experiment contained no strategy labels.
23
Of the same 127 subjects, Simpson found 38 to be rated as individualists and only 10 of these subjects adopted a
cooperative strategy in a one-shot PD.
11
As described previously, the PD game has a dominant strategy of {R2} thereby rendering subject
predictions inconsequential except that they may earn a bonus dollar if they are accurate in their
ex post prediction. There is little theoretical reason to expect that subjects’ predictions will vary
systematically with strategy label treatments, at least in the complete information case. In the
incomplete information case, a subject has no information on “other’s” outcome upon which to
base her prediction (see Figure 3 for an example). However, from a feel-good standpoint – recall
that this is an ex post prediction – subjects in the incomplete information case may be biased
toward thinking that the “other” has selected {R1}, as {R1} on the part of “other” maximizes
payoff for a given own choice.24
Orwellian strategy labels are a complication for both subjects and researchers. Subject
predictions may be based upon any number of personal reasons (e.g., hope, gut instinct,
inference), strategy labels, or on outcomes which are only available in the complete information
treatment. Consequently, three different prediction variables are created. The first is pr_{R1}
which is equal to 1 when a subject predicts “other” has selected {R1} and 0 otherwise.25 Second
is pr_Coop which is equal to 1 when a subject predicts “other” has selected a strategy that
corresponds to the label “cooperate” – {R1} in V and PO treatments and {R2} in NO and OV
treatments – and 0 otherwise. Finally, pr_Focal uses the data from pr_{R1} in the complete
information case as subjects can focus on “other’s” outcomes, and pr_Coop in the incomplete
information treatment as labels are the only information subjects have.
Figure 7 presents a graph of these different predictions by treatment. Columns 1-3 in Figure 7
are constant across all variable definitions while 4a and 5a correspond to pr_{R1}, 4b and 5b
correspond to pr_Coop, and 4c and 5c correspond to pr_Focal. Columns 2 and 3 contain
predictions made by individuals who saw the other player with “normal” labels whereas the
various versions of columns 4 and 5 contain predictions made by individuals who saw the other
player with “Orwellian” labels. Visually, three cases immediately stand out. Data from both the
NV and PO observations under incomplete information are skewed toward {R1}, whereas data
from the PO observations under complete information are skewed toward {R2}. Notice that
none of these data change when different definitions of the prediction variable are adopted as
labels and outcomes align. Moreover, predictions are somewhat skewed toward the nondominant strategy or the cooperative label under the incomplete information condition.
24
Consider Figure 3. As a row player, I may have selected either {R1} or {R2}. Not knowing your payoffs, as a
column player, I may have no feeling what you might do; it is simply a shot-in-the-dark. However, if you selected
{C1} then I can feel good about whatever decision I made – if I selected {R1} then I was not “suckered” and if I
selected {R2} then I make the highest payoff possible.
25
These are predictions of strategy choice irrespective of strategy labels. It was these data that were used to
calculate bonus payoffs. In the complete information treatment, it corresponds to the non-dominant strategy that has
the potential to lead to the Pareto-superior outcome.
12
Figure 8 Ex Post Predictions of Other’s Strategy {about here}
Statistics confirm these visual results. First, a cell-by-cell t-test of the null hypothesis that the
mean of the various dependent variables is equal to 0.5 is conducted. Rejection of this null
hypothesis suggests that predictions deviated systematically from randomization. No matter the
particular form of the dependent variable, the null hypothesis can be rejected only for NV and
PO observations under incomplete information (predictions are skewed toward {R1}) and for
PO observations under complete information (predictions are skewed toward {R2}). A number
of logistic regressions were conducted using the various treatment labels both with and without
the neutral valued labels, and combining observations into those that saw the “other” with
normal labels (from the V and PO data) and those that saw the “other” with Orwellian labels
(from the NO and OV data). 26 While the OV treatment is significant in one case, overall labels
have no significant effect upon predictions. However, in all cases the estimated effect of
incomplete information is to increase prediction of the non-dominant strategy (pr_{R1}), or
whatever strategy is labelled as “cooperation” (pr_Coop), or a combination of both (pr_Focal).
While statistical methods do not clearly indicate how strategy labelling and information
condition might affect predictions, there is important anecdotal evidence to suggest that they
both play a role. Recall that the PO (played using Orwellian labels but saw normal labels) and
NO (played using normal labels but saw Orwellian labels) observations are constructed rather
than conducted. The actual treatments conducted were OR (Orwellian row player) and OC
(Orwellian column player). Table 4 contains the number of subjects who predicted that an
“other” player would adopt the non-dominant {R1} strategy (regardless of label).
Table 4 Predictions of Non-Dominant Play under Data Re-ordering {about here}
The reordering of data has little effect in the incomplete information condition which continues
to be higher than in the complete information case. However, there seems to be a change in the
complete information case. Subjects who played using Orwellian labels and saw others with
normal labels predict that others will play {R1} less often than those who played using normal
labels and saw others with Orwellian labels. Replicating these treatments will lead to additional
insight into how subjects use information to form predictions.
5. Conclusion
While both valence and pure framing effects have received considerable analysis in social
dilemma experiments, only three studies have focussed on the effects of explicit strategy
labelling. The results from these three experiments are mixed and suggest that strategy labels
may shift decisions toward non-dominant strategies. The analysis is complicated because in the
26
These regressions are discussed but go unreported for the sake of brevity. Results are available from the author.
13
two experiments in which there are any effects, the data is generated in an iterated PD
environment which does not have a straightforward equilibrium prediction, and because in both
experiments the role of the other player was misrepresented to subjects.
A new experiment is designed which uses a one-shot PD game to compare decisions under
conditions of neutral labels, valued labels, and Orwellian-valued (reversed) labels with both
complete and incomplete information. Information condition does not systematically affect
strategy selection. There is evidence however, that subjects are more likely to select a strategy if
it is labelled {cooperate} as opposed to {cheat}. This effect is strongest when Orwellian labels
are used and {cooperate} corresponds to the dominant strategy. Re-sorting data from ½Orwellian sessions according to label ordering clearly indicates that strategy labelling affects
decisions.
In this experiment, ex post predictions of the decision of the other player are also elicited using
salient methods. Predictions are more self-serving under incomplete information treatments, but
this does not go against theoretical expectations. Discerning how predictions are made is
complicated by the fact that, under complete information, subjects may focus upon outcome or
strategy label or a combination of both, and all subjects need not be alike. Once again the
division of data from the ½-Orwellian sessions indicates that some sort of systematic change is
taking place, but additional study is necessary to draw firm conclusions.
This experiment shows that strategy labels change people’s behaviour. More importantly, it
shows that spin can be used to direct behaviour in a social dilemma. Social dilemmas reflect a
tension we all feel in our day-to-day interactions: a call to act in a collective manner so as to
maximize joint outcomes versus the desire to act in one’s self-interest. Traditional labels, those
that label the non-dominant strategy as {cooperate} or something similar, those labels that
correspond to researchers’ common interpretation of behaviour in social dilemmas, reinforce
some people’s natural tendency to search for joint outcome maximization. Orwellian labels,
those that frame individualism as collective action, enhance people’s selection of the dominant
strategy. This result is especially evident in the data from this experiment and warns of the
potential harm that can be done to social welfare if it becomes standard practise to use Orwellian
labels.27
Future research should be conducted to understand how people form predictions in this complex
environment and, once formed, how these predictions are used. The existing data can be used to
more fully explore predictions and its link to strategy selection. As always, it would be useful to
collect more data and especially data generated in the ½-Orwellian sessions. Given the
interesting patterns that resulted from the re-sorting of these data, it is here where the greatest
27
The use of language to influence choice is well-documented; consider the case of pollster, Frank Luntz. To see
examples of how doublespeak is used in our culture, see (the similarly-named) Lutz (2000).
14
insights are likely to be gained. It would also be useful to elicit subject’s social values (Simpson,
2004) and risk attitudes (de Heus et al., 2010) as extra explanatory variables and a possible
explanation for the significant amount of non-dominant strategy selection observed in the neutral
valued session.
15
Tables
Table 1 Experimental Design Table
Treatment
Strategy Labels
CI
II
Neutral (N)
R1 = C1 = “A$”; R2 = C2 = “@#”
10 obs
10 obs
Valued (V)
R1 = C1 = “Cooperate”; R2 = C2 = “Cheat” 10 obs
10 obs
Orwellian Row (OR)
R1 = C2 = “Cheat”; R2 = C1 = “Cooperate” 10 obs
10 obs
Orwellian Column (OC)
R1 = C2 = “Cooperate”; R2 = C1 = “Cheat” 10 obs
10 obs
COR+ROC (NO)
Had normal labels in a ½-Orwellian game
10 obs
10 obs
ROR+COC (PO)
Had Orwellian labels in a ½-Orwellian
game
10 obs
10 obs
R1 = C1 = “Cheat”; R2 = C2 = “Cooperate” 10 obs
10 obs
Orwellian Valued (OV)
Table 2 Summary Data by Information Condition
Males
Faculty (Arts/Business/Science/Nursing)
Non-Dominant Decision
Non-Dominant Prediction (in outcomes)
Cooperate Prediction (in labels)
Prediction = Decision (in outcomes)
Prediction = Decision (in labels)
Non-Rationalizable Prediction
Correct Prediction
Pay (SD)
Pay + Bonus (SD)
Information
Complete
Incomplete
18
12
14/11/8/17
13/9/14/8
20
17
18
34
22
32
36
19
28
29
8
7
22
27
$3.80 ($2.21)
$3.68 ($2.27)
$4.24 ($2.14)
$4.22 ($2.49)
16
Fisher Exact
Test p-value
0.679
0.003
0.070
0.001
1.000
1.000
0.424
0.790
0.966
Table 3 Logistic Regression: Decision upon Treatments (Standard Errors)
constant
V
OC
OR
NO
PO
OV
Valued
OValued
II
Nobs
LR
prob > χ2
Psuedo-R2
(1) {R2}
0.2653 (0.5043)
-0.8150 (0.6472)
0.0000 (0.6471)
0.4439 (0.6697)
1.3342 (0.7764)*
0.2843 (0.4364)
100
10.11*
0.0721
0.0767
(2) {R2}
0.2378 (0.5130)
-0.8168 (0.6480)
-1.0318 (0.6568)
2.5491 (1.1246)**
1.3364 (0.7770)*
0.3412 (0.4786)
100
27.71***
0.0000
0.2103
(3) {R2}
0.2390 (0.5127)
-0.9228 (0.5635)
1.8003 (0.6992)***
0.3388 (0.4770)
100
26.45***
0.0000
0.2007
Notes: Rejection of zero effect at * 10% level, ** 5% level, *** 1% level.
Table 4 Predictions of Non-Dominant Play under Data Re-ordering {about here}
CI
II
OR
3
9
OC
3
8
played
saw
NO
5
7
{coop, cheat}
{cheat, coop}
17
PO
1
10
{cheat, coop}
{coop, cheat}
Saw other’s pay
Saw ? for other’s pay
Figures
Figure 1 A Generic PD Game
Row
Player
Column Player
Left
Right
R=5
R=1
C=5
C=7
R=7
R=3
C=1
C=3
Up
Down
Figure 2 A Generic Complete Information PD Game
Column Player
ROW
PLAYER
R1
R2
C1
C2
R=5
C=5
R=7
C=1
R=1
C=7
R=3
C=3
Figure 3 A Generic Incomplete Information PD Game
COLUMN PLAYER
R1
Row Player
R2
18
C1
C2
R=?
C=5
R=?
C=1
R=?
C=7
R=?
C=3
Figure 4 Non-Dominant Decisions by Treatment
19
Figure 5 Non-Dominant Decisions by Treatment (Relabelled Data)
20
Figure 6 Non-Dominant Decisions by Grouped Treatment
Figure7 A Generic Transformed PD AD Game
Column Player
R1
Row Player
R2
21
C1
C2
R=7
C=7
R=5
C=1
R=1
C=5
R=3
C=3
Figure 8 Ex Post Predictions of Other’s Strategy
22
Sample Questionnaire
OR_II_C
Subject ID:
_______________________
Thank you for your participation. Please answer the questionnaire below.
1. What is your gender? (circle one)
Male
Female
2. In which Faculty are you enrolled? (circle one)
Arts
Business
Sciences
Other
3. What is your main area of study – your major, or the courses you most-identify with?
______________________________________________________________________________
Below is a copy of the table you faced earlier as a Column Player.
COLUMN PLAYER
COOPERATE
CHEAT
R=?
R=?
C=5
C=7
R=?
R=?
C=1
C=3
Cheat
Row Player
Cooperate
4. What action do you predict the Row Player you are paired with chose? (circle one)
** Please note that you will receive a bonus payment of $1 if you are correct in your prediction.
Cheat
Cooperate
5. What degree of certainty do you place on your prediction above? A value of 50 is just a guess,
whereas as a value of 100 means you are absolutely certain of your choice. Chose a value
between 50 and 100?
__________________________________
23
References
Andreoni, J. (1995). Warm-glow versus cold-prickle: The effects of positive and negative
framing on cooperation in experiments. Quarterly Journal of Economics. 110(1): 1-21.
Batson, C.D. and T. Moran. (1999). Empathy-induced altruism in a prisoner’s dilemma.
European Journal of Social Psychology. 29: 909-924.
Brewer, M. and R. Kramer. (1986). Choice behaviour in social dilemmas: Effects of social
identity, group size, and decision framing. Journal of Personality and Social Psychology. 50(3):
543-549.
Chwastiak, M. (2001). Taming the untamable: planning, programming and budgeting and the
normalization of war. Accounting, Organizations and Society. 26: 501–519.
Dawes, R., J. McTavish, and H. Shaklee. (1977). Behavior, communication, and assumptions
about other people’s behaviour in a commons dilemma situation. Journal of Personality and
Social Psychology. 35(1): 1-11.
Dawes, R. (1980). Social dilemmas. Annual Reviews of Psychology. (31): 169-193.
Dufwenberg, M., S. Gächter, and H. Hennig-Schmidt. (2010). The Framing of Games and the
Psychology of Play. CeDEx Discussion Paper 2010-16. (Available online
http://www.nottingham.ac.uk/cedex/documents/papers/2010-16.pdf, accessed 30 September
2010.
Eiser, J.R. and K. Bhavnani. (1974). The effect of situational meaning on the behaviour of
subjects in the Prisoner’s Dilemma game. European Journal of Social Psychology. 4(1): 93-97.
Ellingsen, T., M. Johannesson, S. Munkhammar, and J. Möllerström. (2009). Why Labels Affect
Cooperation. Unpublished manuscript. (Available online
http://economics.uchicago.edu/pdf/Ellingsen_042709.pdf, accessed 8 September 2010).
Elliott, C. and D. Hayward. (1998). The expanding definition of framing and its particular impact
on economic experimentation. Journal of Socio-Economics. 27(2): 229-243.
Elliott, C., D. Hayward, and S. Canon. (1998). Institutional framing: Some experimental
evidence. Journal of Economic Behavior & Organization. 35: 455-464.
Fleishman, J. (1988). The effects of decision framing and others’ behaviour on cooperation in a
social dilemma. Journal of Conflict Resolution. 32(1): 162-180.
24
Flood, M. (1952). Some experimental games. RAND Research Memorandum: RM-789-1.
(Available online http://www.rand.org/pubs/research_memoranda/2008/RM789-1.pdf, accessed
23 October 2010).
de Heus, P., N. Hoogervorst, and E. Van Dijk. (2010). Framing prisoners and chickens: Valence
effects in the prisoner’s dilemma and the chicken game. Journal of Experimental Social
Psychology. 46: 736-742.
Janssen, M. (2008). Evolution of cooperation in a one-shot Prisoner’s Dilemma based on
recognition of trustworthy and untrustworthy agents. Journal of Economic Behavior &
Organization. 65: 458-471.
Johnston, M., C. Markey, and L. Messé. (1973). Sex difference in labelling effects on behaviour
in the prisoner’s dilemma game. Proceedings of the Annual Convention of the American
Psychological Association: 323-324.
Kahneman, D. and A. Tversky. (1984). Choices, values, and frames. American Psychologist.
39(4): 341-350.
Kay, A. and L. Ross. (2003). The perceptual push: The interplay of implicit cues and explicit
situational construals on behavioural intentions in the Prisoner’s Dilemma. Journal of
Experimental Social Psychology. 39: 634-643.
Kuhn, S. (2009). "Prisoner's Dilemma", The Stanford Encyclopedia of Philosophy (Spring 2009
Edition), Edward N. Zalta (ed.). (Available online
http://plato.stanford.edu/archives/spr2009/entries/prisoner-dilemma/, accessed 20 October 2010).
Larrick, R. and S. Blount. (1997). The claiming effect: Why players are more generous in social
dilemmas than in ultimatum games. Journal of Personality and Social Psychology. 72(4); 810825.
Liberman, V., S. Samuels, and L. Ross. (2004). The name of the game: Predictive power of
reputations versus situational labels in determining prisoner’s dilemma game moves. Personality
and Social Psychology Bulletin. 30:1175-1185.
Lutz, W. (2000). Nothing in life is certain except negative patient care outcome and revenue
enhancement. Journal of Adolescent & Adult Literacy. 44(3): 230-233.
Murnighan, J.K. and A. Roth. (1983). Expecting continued play in prisoner’s dilemma games.
Journal of Conflict Resolution. 27(2): 279-300.
Orwell, G. (1981). Nineteen Eighty-Four. Signet Classics/Penguin Books: Toronto, ON.
25
Oskamp, S. and D. Perlman. (1965). Factors affecting cooperation in a prisoner’s dilemma game.
Journal of Conflict Resolution. 9(3): 359-374.
Pigou, A. (1920). The Economics of Welfare. MacMillan and Co., Ltd.: London. (Available
online http://www.archive.org/stream/economicsofwelfa00pigouoft#page/n5/mode/2up, accessed
5 November 2010).
Rege, M. and K. Telle. (2004). The impact of social approval and framing on cooperation in
public good situations. Journal of Public Economics. 88: 1625-1644.
Rilling, J., D. Gutman, T. Zeh, G. Pagnoni, G. Berns, and C. Kilts. A neural basis for social
cooperation. Neuron. 35: 395-405.
Schelling, T. (1960). The Strategy of Conflict. Harvard University Press: Cambridge, MA.
Simpson, B. (2004). Social values, subjective transformations, and cooperation in social
dilemmas. Social Psychology Quarterly. 67(4): 385-395.
Straffin, P., Jr. (1980). The prisoner’s dilemma. UMAP Journal. 1: 101-103.
Swope, K., J. Cadigan, P. Schmitt, and R. Shupp. (2008). Personality preferences in laboratory
economics experiments. The Journal of Socio-Economics. 37: 998-1009.
Tucker, A. (1950). A Two-Person Dilemma. Unpublished notes, Stanford University (presented
in Straffin above).
Wolpert, D., J. Jamison, D. Newth, and M. Harre. (2010). Strategic Choice of Preferences: The
Persona Model. Federal Reserve Bank of Boston: Working Paper 10-10. (Available online
http://www.bos.frb.org/economic/wp/wp2010/wp1010.pdf, accessed 10 October 2010).
Zhong, C., J. Loewenstein, and J.K. Murnighan. (2007). Speaking the same language: The
cooperative effects of labeling in the prisoner’s dilemma. Journal of Conflict Resolution. 51(3):
431-456.
26