Noname manuscript No.
(will be inserted by the editor)
Reciprocity and trust:
Personality psychology meets behavioral economics
Ricardo Andrés Guzmán · Rodrigo Harrison ·
Nureya Abarca · Mauricio G. Villena
Received: date / Accepted: date
Abstract We propose a model of strong reciprocity and trust that combines elements of personality psychology and behavioral economics. In the model, positive reciprocity and negative
reciprocity are components of individual utility functions, while trust is an individual bias that
distorts the beliefs about the trustworthiness of others. Underlying personality traits determine
the functional form of the utility functions and the magnitude of the biases.
We tested the model by means of an economic experiment, using 212 college students as
experimental subjects. First, each subject completed a psychometric questionnaire to measure
his levels of positive reciprocity, negative reciprocity, and trust. Following this, the subjects
played 65 rounds of a sequential prisoner’s dilemma with random re-matching and payoffs that
changed from round to round. From the game behavior of each subject we estimated his utility
function and the bias in his beliefs. The experimental results support the hypotheses of the model;
the psychometric measures of reciprocity determined the individual utility functions, while the
psychometric measures of trust determined the individual biases.
Keywords Strong reciprocity · trust · personality · psychometrics · revealed preferences.
JEL codes: C72, C92, D03.
Ricardo Andrés Guzmán, corresponding author.
Centro de Investigación en Complejidad Social (CICS), Facultad de Gobierno, UDD. Address: Avenida Plaza 680,
San Carlos de Apoquindo, Las Condes, Santiago, Chile. Tel.: +562 327-97-01 E-mail: [email protected]
Rodrigo Harrison
Instituto de Economı́a, Pontificia Universidad Católica de Chile. Address: Avenida Vicuña Mackenna 4860, Macul,
Santiago, Chile. E-mail: [email protected]
Nureya Abarca
Escuela de Administración, Pontificia Universidad Católica de Chile. Address: Avenida Vicuña Mackenna 4860,
Macul, Santiago, Chile. E-mail: [email protected]
Mauricio G. Villena
Escuela de Negocios, Universidad Adolfo Ibáñez. Address: Diagonal Las Torres 2640, Peñalolén, Santiago, Chile.
E-mail: [email protected]
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Ricardo Andrés Guzmán et al.
1 Introduction
Personality psychology and behavioral economics share an interest in strong reciprocity and trust
(Fehr & Gächter 2000; Perugini et al., 2002; Sobel 2005). Each discipline has approached these
phenomena using its proprietary set of models and empirical methods. Their relative advantages
and disadvantages suggest that a synthesis between both approaches could be useful to further
our understanding of strong reciprocity and trust (Almlund et al. 2011; Caplan, 2003; Ferguson et
al. 2011; Heckman 2011; Heckman et al. 2008). Personality psychology could contribute its ability
to describe what economists call preferences and beliefs in terms of a reduced set of personality
traits. These traits could be measured using psychometric techniques, which have shown high
predictive power in a wide range of real-life behaviors, including reciprocal and trusting behaviors.
Behavioral economics, in turn, could contribute a theoretical framework that accounts for the
situation (“the game”) and material incentives. This framework consists of utility functions that
allow for heterogeneity in reciprocal preferences and probabilistic models of individual beliefs,
plus game theoretic models representing social interactions in which reciprocity and trust play a
role; for example, the trust game, the ultimatum game, and the prisoner’s dilemma.
Along these lines, we propose a synthetic model of reciprocity and trust that connects elements
of personality psychology and behavioral economics. The model has four parts: (1) a sequential
prisoner’s dilemma that represents a scenario of reciprocal interaction (Clark & Sefton 2001);
(2) a utility function with reciprocal preferences that depend on personality traits (Charness &
Rabin 2002); (3) a model of subjective (probabilistic) beliefs about how likely other players are
to cooperate whose bias also depends on personality traits, and (4) a quantal response function
(McKelvey & Palfrey 1998) describing how players choose among three alternative strategies,
to cooperate conditionally, to cooperate unconditionally, and to defect unconditionally. In other
words, this model aims to capture the way in which personality manifests itself given different
incentives in the context of a prisoner’s dilemma. The model also aims to explain reciprocal
preferences and beliefs of trustworthiness as functions of personality traits.
We also report an empirical test of the synthetic model. This test combines empirical methods
of both disciplines: (1) a psychometric questionnaire specially designed to measure positive reciprocity, negative reciprocity, and trust (Dohmen et al. 2008), and (2) an economic experiment, in
which the subjects played a sequential prisoner’s dilemma with random re-matching and payoffs
that changed from round to round. From the game behavior of each experimental subject we
estimated his utility function and the bias in his probabilisitic beliefs. The experimental results
support the hypotheses of the model: the psychometric measures of reciprocity determined the
individual utility functions, while the psychometric measures of trust determined the individual
biases.
The rest of this paper proceeds as follows. In Section 2 we briefly compare the approaches of
personality psychology and behavioral economics to the study of strong reciprocity and trust. In
Section 3 we develop the synthetic model. In Section 4 we present the materials and methods of
Reciprocity and trust: Personality psychology meets behavioral economics
3
the empirical test. In Section 5 we report the results of the study. Finally, in Section 6 we offer
some conclusions.
2 Two alternative approaches to strong reciprocity and trust
In personality psychology, positive reciprocity, negative reciprocity, and trust are modeled as
personality traits, or as combinations of higher-order personality traits (Dohmen et al. 2008;
Perugini et al. 2003). Psychometricians typically measure personality traits using self-report
questionnaires. They also look for statistical relations between personality traits and behaviors and life outcomes. Recent studies have found that measured levels of positive and negative
reciprocity predict various behaviors in the workplace, earned incomes, and probability of employment (Dohmen et al. 2009; Dur et al. 2010; Raymond et al. 2012). Trust as a personality
trait, on the other hand, has been widely studied (Jones et al. 1997). It has predictive power
in many aspects of life, including individual economic behaviors and performance (Butler et al.
2009).
Personality traits predict a wide range of behaviors and life outcomes, averaged over many
situations and occasions (Funder, 2008; Roberts 2009). They are, however, bad predictors of
behaviors and outcomes in specific situations. This is because personality models do not take
into account the behavioral effects of context and material incentives (Funder 2008). Recently,
psychologists have begun to study how personality manifests itself in different situations (e.g.,
Fleeson 2007; Fournier et al. 2008), but not how personality is modulated by with economic
incentives.
More fundamentally, personality models have been criticized for having a tenuous theoretical
basis (Almlund et al. 2011; Blanton & Jaccard 2006). Also, psychometrics faces severe identification problems: it can detect correlations between personality traits and behaviors or outcomes,
but it often fails to establish causality (Borghans et al. 2011; Almlund et al. 2011; Heckman
2011). Furthermore, self-report questionnaires are vulnerable to misrepresentation: examinees
can manipulate their answers to present a desirable image, or they may disclose a distorted
self-image (Viswesvaran & Ones 1999).
In behavioral economics, positive and negative reciprocity are modeled as social preferences
(Cox et al. 2007; Dufwenberg & Kirchsteiger, 2004; Falk & Fischbacher 2006; Rabin 1993). Trust,
on the other hand, is modelled as an individual probabilistic belief about the trustworthiness
of others (Ashraf et al. 2006; Buchan et al. 2008; Eckel & Wilson 2004; Fetchenhauer & Dunning 2009). To measure social preferences and trust, researchers conduct experiments in which
people play games for money, such as the trust game, the ultimatum game, and the prisoner’s
dilemma (Camerer & Fehr 2004). Some researchers use this experimental data to classify individual utility functions into types: selfish, altruistic, inequity-averse, positively reciprocal, negatively
reciprocal, etc. (e.g., Burlando & Guala 2005; Charness & Rabin 2002; Engelmann & Strobel
2004; Fischbacher et al. 2001; Kurzban & Houser 2001; Rodrı́guez-Sickert et al. 2008). Other re-
4
Ricardo Andrés Guzmán et al.
searchers use experimental data to estimate the complete functional form of the utility functions
(e.g., Andreoni & Miller 2002; Andreoni et al. 2009; Charness & Rabin 2002; Fisman et al. 2005;
Goeree et al. 2002).
Compared to personality psychology, behavioral economics has a firmer theoretical basis,
which is provided by choice theory and game theory (Camerer et al. 2003, part two). Unlike
personality models, choice theory and game theory take into account the behavioral effects of
context (“the game”) and material incentives. Also, economic experiments can identify causality
by means of controlled variation (Falk & Heckman 2009), while the double-anonymous experimental design plus the use of material incentives discourage the misrepresentation of preferences
and beliefs (Bardsley et al. 2010, Chapter 6 and p. 232).
Nevertheless, behavioral economics has a serious weakness: many of its experimental findings
lack external validity. This means that the experimental findings do not extend to “real life”, at
least not in the direct, unconditional way demanded by some critics of experimental economics.
The lack of external validity is particularly prevalent in experiments measuring social preferences
(Levitt & List 2007); there are, however, some positive findings. For example, a recent study by
Barr and Serneels (2009) found a bicausal relation between worker productivity and reciprocating
behavior in the investment game.
In comparison to experimental economics, psychometrics has a much better record in predicting real-life behavior. To our knowledge, only one study has done the comparison directly.
Anderson et al. (2011) compared the predictive power of psychometric measures of personality
and experimental estimates of risk-aversion and delay-discounting. The authors found that, in
combination, personality measures outperformed estimated economic preferences in predicting
credit scores, job persistence, driving accidents, body-mass index, and smoking habits.
The predictive power of personality traits is not limited to real-life behaviors: personality
traits also predict behavior in many economic experiments (Brocklebank et al. 2011). These
experiments include the dictator game (Ben-Ner et al. 2004; Ben-Ner & Kramer 2011), the trust
game (Evans & Revelle 2008; Ben-Ner & Halldorsson 2010; Burks et al. 2004; Gunnthorsdottir et
al. 2002), the ultimatum game (Brandstätter & Königstein 2001), the prisoner’s dilemma (Boone
et al. 1999, 2002; Hirsh & Peterson 2009; Pothos et al. 2011), and the public good game (Kurzban
& Houser 2001; Perugini et al. 2010). There are few negative findings (Swope et al. 2008).
3 A model of strong reciprocity and trust
The model has four parts, which we describe in the following sections: (1) a sequential prisoner’s
dilemma that represents a scenario of reciprocal interaction (Section 3.1); (2) a utility function with reciprocal preferences that depend on personality traits (Section 3.2); (3) subjective
probabilistic beliefs about how likely other players are to cooperate whose bias also depends
on personality traits (Section 3.3), and (4) a quantal response function (Section 3.4) describing
Reciprocity and trust: Personality psychology meets behavioral economics
5
how players choose among three alternative strategies, to cooperate conditionally, to cooperate
unconditionally, and to defect unconditionally.
3.1 A sequential prisoner’s dilemma
Two players participate in a sequential prisoner’s dilemma (Clark & Sefton, 2001). The players
can perform two actions: cooperate or defect. One player moves first and decides, blindly, whether
to cooperate or not. Before knowing this decision, the second mover chooses his response among
three alternative strategies:
1. Cooperate unconditionally, regardless of whether the first mover has cooperated or defected.
2. Cooperate conditionally, if and only if the first mover has cooperated.
3. Defect unconditionally, regardless of whether the first mover has cooperated or defected.
The extensive form of the game is presented in Figure 1. Letters “c” and “d” denote the
players’ actions, and function π(·) represents the money payoffs of the game. The payoffs are
symmetric: if the first mover performs action a1 , and the second mover responds with action a2 ,
the first mover obtains π(a1 , a2 ) while the second mover obtains π(a2 , a1 ). The money payoffs
satisfy the following inequalities, which imply that the game is a prisoner’s dilemma:
π(d, c) > π(c, c) > π(d, d) > π(c, d) ≥ 0.
If the players maximized expected income, the game would have a unique Nash equilibrium
in strictly dominant strategies: the first mover defects blindly and the second mover defects
unconditionally.
3.2 A utility function with reciprocal preferences
We focus our attention on the second mover, because he has the option to reward or punish the
actions of the first mover; that is, to reciprocate the behavior of the first mover. The second
mover’s utility function is given by

(1 − r+ )π + r+ π
2
1
u(π2 , π1 ) =
(1 + r− )π − r− π
2
1
if the 1st mover cooperated blindly,
(1)
if the 1st mover defected blindly.
This is an adapted version Charness and Rabin’s utility function (Charness & Rabin 2002). In
the formula, π1 and π2 are the payoffs obtained by the first and the second mover, respectively.
Parameter r+ represents the second mover’s positive reciprocal preference, while r− represents
his negative reciprocal preference. In principle, we let r+ , r− ∈ R. The second mover’s utility will
be strictly increasing in his own payoff if and only if r+ < 1 and r− > −1.
6
Ricardo Andrés Guzmán et al.
π(c,c), π(c,c)
2nd
mover
Cooperate
conditionally
π(c,c), π(c,c)
π(c,d), π(d,c)
1st
mover
π(d,c), π(c,d)
Cooperate
conditionally
π(d,d), π(d,d)
π(d,d), π(d,d)
Fig. 1: The sequential prisoner’s dilemma. The players can perform two actions: cooperate (c)
or defect (d). The payoffs are symmetric: if the first mover performs action a1 , and the second
mover responds with action a2 , the first mover obtains π(a1 , a2 ) while the second mover obtains
π(a2 , a1 ). The payoffs satisfy π(d, c) > π(c, c) > π(d, d) > π(c, d) ≥ 0.
The utility function given in equation (1) is flexible enough to capture many intuitive preference structures. Six archetypal cases are illustrative:
1. If r+ = r− = 0, the second mover is selfish:
u(π2 , π1 ) = π2 .
2. If r+ ∈ (0, 1] and r− = −r+ , the second mover is an altruist:
u(π2 , π1 ) = (1 − r+ )π2 + r+ π1 .
3. If r− > 0 and r− = −r+ , the second mover is spiteful:
u(π2 , π1 ) = (1 + r− )π2 − r− π1 .
4. If r+ ∈ (0, 1] and r− = 0, the second mover is a pure positive reciprocator:

(1 − r+ )π + r+ π if the 1st mover cooperated blindly,
2
1
u(π2 , π1 ) =
π
if the 1st mover defected blindly.
2
Reciprocity and trust: Personality psychology meets behavioral economics
7
5. If r− > 0 and r+ = 0, the second mover is a pure negative reciprocator.

π
if the 1st mover cooperated blindly,
2
u(π2 , π1 ) =
(1 + r− )π − r− π if the 1st mover defected blindly.
2
1
6. If r+ ∈ (0, 1] and r− > 0, the second mover is simultaneously a positive and a negative
reciprocator [see equation (1)].
The second mover’s reciprocal preferences depend on two personality traits that represent his
underlying levels of positive and negative reciprocity. Let R+ be his positive reciprocity trait, and
let R− be his negative reciprocity trait, where R+ , R− ∈ R. Both traits are random variables and
may or may not be correlated. Assume that E[R+ ] = E[R− ] = 0, and var[R+ ] = var[R− ] = 1.
Reciprocal preferences relate to reciprocity personality traits in the following way:
T +
+ +
+ −
r+ = ρ+
0 + ρ1 R + ρ2 R = R ρ ,
(2)
T −
− +
− −
r − = ρ−
0 + ρ1 R + ρ2 R = R ρ ,
(3)
where ρ+ , ρ− ∈ R3 are vectors of parameters common to all members of the population. Since
−
E[R+ ] = E[R− ] = 0, parameters ρ+
0 and ρ0 are the reciprocal preferences of the average second
mover.
We formulate the following hypotheses regarding the relation between reciprocal preferences
and reciprocity traits.
Hypothesis 1 The average second mover’s utility function is strictly increasing in his payoff:
ρ+
0 < 1,
(4)
ρ−
0
(5)
> −1.
Hypothesis 2 The average second mover is a positive and negative reciprocator:
ρ+
0 ∈ (0, 1],
(6)
ρ−
0 > 0.
(7)
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Ricardo Andrés Guzmán et al.
Hypothesis 3 The positive reciprocal preference is increasing in the positive reciprocity trait,
and does not depend on the negative reciprocity trait:
ρ+
1 > 0,
(8)
ρ+
2 = 0.
(9)
Hypothesis 4 The negative reciprocal preference is increasing in the negative reciprocity trait,
and does not depend on the positive reciprocity trait:
ρ−
2 > 0,
(10)
ρ−
1 = 0.
(11)
3.3 Subjective beliefs
Let p ∈ [0, 1] be the true probability that the first mover cooperates blindly. The second mover
believes this probability is µ, which is given by
µ=
p exp(t)
,
1 − p + p exp(t)
(12)
where t ∈ R is the second mover’s trust coefficient. By construction, µ ∈ [0, 1] and µ is an
increasing function of t. This means that trustful second movers have large values of t, while
distrustful second movers have low values of t.
Three cases are worth noting:
1. If t = 0, the second mover guesses the true value of p; that is, µ = p.
2. If t > 0, the second mover overestimates p; that is, µ > p.
3. If t < 0, the second mover underestimates p; that is, µ < p.
The second mover’s trust coefficient depends on a personality trait that represents his underlying level of trust. Let T be his trust trait, where T ∈ R. The trust trait is a random variable, and
may or may not be correlated to the reciprocity traits. Assume that E(T ) = 0, and var(T ) = 1.
The trust coefficient relates to the trust trait in the following way:
t = τ0 + τ1 T = TT τ,
(13)
where τ ∈ R2 is a vector of parameters common to all members of the population. Since E(T ) = 0,
parameter τ0 is the trust coefficient of the average second mover.
We formulate the following hypotheses regarding the relation between the trust coefficient
and the trust trait.
Hypotheses 5 The trust coefficient is increasing in the trust trait:
τ1 > 0.
(14)
Reciprocity and trust: Personality psychology meets behavioral economics
9
3.4 The quantal response function
The second mover chooses his strategy non-deterministically, skewing the probabilities toward
the strategies that provide higher expected utility. Let S = {CU, CC, DU} be the set of available
strategies, where CU means “cooperate unconditionally,” CC means “cooperate conditionally,”
and DU means “defect unconditionally.” Denote by E[u(s)] the subjective expected utility from
choosing strategy s, and by q(s) the probability of choosing strategy s. This probability is given
by a quantal response function:
exp(λ E[u(s)])
,
x∈S exp(λ E[u(x)])
q(s) = P
(15)
where λ > 0 is a parameter common to all members of the population.
By construction, q(s) is increasing in E[u(s)]. Also, the larger λ, the more likely the second
mover will choose the strategy that maximizes his expected utility. In the limiting case in which λ
tends to infinity, the second mover acts as an expected utility maximizer. In contrast, if λ equals
zero, he chooses all strategies with equal probability. For these reasons, we call λ the rationality
parameter.
To calculate the expected utility of the different strategies, we combine the payoffs in Figure
1, the utility function defined in equation (1), the subjective probability defined in equation (12),
and the definitions of r+ , r− , and t given in equations (2), (3), and (13):
h
i
E[u(CU)] = µπ(c, c) + (1 − µ) (1 + RT ρ− )π(c, d) − RT ρ− π(d, c)
E[u(CC)] = µπ(c, c) + (1 − µ) π(d, d)
h
i
E[u(DU)] = µ (1 − RT ρ+ )π(d, c) + RT ρ+ π(c, d) + (1 − µ) π(d, d),
where
µ=
p exp(TT τ)
.
1 − p + p exp(TT τ)
(16)
(17)
(18)
(19)
Together, equations (15)–(19) constitute a model of strategic behavior in which the probability
of the second mover choosing a particular strategy is a function of his personality traits and the
payoffs of the game. The values of the parameters (ρ+ , ρ− , τ, and λ) are to be determined
empirically.
4 Materials and methods
4.1 Subjects and procedure
The experimental sessions took place at the Pontifical Catholic University of Chile between May
and June 2010. A total of 212 college students from various academic majors volunteered as
subjects. They were 18.9 years old on average, with a standard deviation of 1.9. Ninety-two
10
Ricardo Andrés Guzmán et al.
of the subjects were female, and all subjects were native Spanish speakers. We conducted 10
experimental sessions, which were attended by between 16 and 24 subjects each. The sessions
were carried out in a computer room equipped with z-Tree, a program for economic experiments
(Fischbacher 2007). We used a double-anonymous experimental design to mitigate the effects of
the social desirability bias, and random re-matching to eliminate the incentives for reputation
building (Bardsley et al. 2010). No communication was allowed between the subjects during the
experiment.
Each experimental session was divided into two stages. At the beginning of each stage, the
session coordinator distributed printed instructions which he then read aloud (the original instructions written in Spanish, plus an English translation, are available in an online appendix).
After reading the instructions, the coordinator answered questions from the subjects, and begun
the first stage.
In the first stage of the experiment the subjects completed a psychometric questionnaire
specifically designed to measure reciprocity and trust. The reciprocity/trust psychometric questionnaire was taken from the 2005 wave of the German Socio-Economic Panel (Dohmen et al.
2008). This questionnaire includes nine statements: three refer to positive reciprocity, three refer to negative reciprocity, and three refer to trust. Table 1 displays the nine statements in the
order presented to the subjects. Since all subjects were native Spanish speakers, we translated
the questionnaire into Spanish (the translation is available in an online appendix). Each subject
was asked to rate, on a 5-point Likert scale, his degree of agreement with each statement. Additionally, the subjects completed the NEO-PI-R personality inventory (Costa & McCrae 1985),
whose results we do not analyze in this paper. After finishing the first stage, the subjects took a
five-minute break.
During the second stage of the experiment, the subjects played 65 rounds of a sequential
prisoner’s dilemma: 5 practice rounds, numbered −5 to −1, followed by 60 rounds for real money,
numbered 1 to 60. The payoffs of the game changed from round to round, as shown in Table 2.
At the beginning of each round, the subjects were randomly matched. Since the number of
rounds exceeded the number of subjects, two subjects could play together more than once during
the experiment. Anonymity prevented the subjects from knowing when this happened.
In each round, each subject had to make two decisions: (1) what to do if he was given the
role of first mover, and (2) what to do if he was given the role of second mover. Recall that the
options for a first mover are to cooperate or defect blindly, and the options for a second mover
are to cooperate unconditionally, to cooperate conditionally, or to defect unconditionally. The
subjects had to make their decisions in private and before knowing the role that they would play
in the current round.
Once both members of a pair made their decisions, z-Tree “flipped a coin” and assigned the
roles of first and second mover. The subjects’ payoffs were computed accordingly. At this point,
each subject was informed of the role he was given, whether his partner cooperated or not, and
their respective payoffs. The subject was also informed of his accumulated earnings so far.
Reciprocity and trust: Personality psychology meets behavioral economics
11
Table 1: The reciprocity/trust psychometric questionnaire
Item
Statemement
Trait
1
In general, one can trust people.
Trust
2
If someone does me a favor, I am prepared to return it.
Positive reciprocity
3
If I suffer a serious wrong, I will take revenge as soon
as possible, no matter what the cost.
Negative reciprocity
4
These days you cannot rely on anybody else.
Trust
5
I am ready to undergo personal costs to help somebody
who helped me before.
Positive reciprocity
6
If somebody puts me in a diffcult position, I will do the
same to him/her.
Negative reciprocity
7
When dealing with strangers it is better to be careful
before you trust them.
Trust
8
I go out of my way to help some body who has been
kind to me before.
Positive reciprocity
9
If somebody insults me, I will insult him/her back.
Negative reciprocity
Note: Items 2 and 3 are reverse coded. The third column was not presented to the subjects.
The subjects were paid in private upon leaving the session. No show-up fee was offered to
the subjects. Total game earnings ranged between CLP 10,000 (≈ USD 20) and CLP 20,000 (≈
USD 40), approximately (CLP is the acronym for Chilean pesos).
4.2 Method of estimation
We estimated the model using the maximum likelihood method.
Let yij (s) = 1 if subject i chose strategy s in round j, and yij (s) = 0 if he did not. The
log-likelihood function is defined as follows:
L(β) =
212 X
60 X
X
yij (s) ln qij (s, β),
(20)
i=1 j=1 s∈S
where qij (s, β) probability that subject i chooses strategy s in round j, S = {UC, CC, DU} is
the set of available strategies, and β is a vector of parameters. This vector of parameters is given
by

ρ+

 −
ρ 

β=
 τ ,
 
λ
and it must be determined empirically by maximizing L(β).
12
Ricardo Andrés Guzmán et al.
Table 2: Payoffs of the sequential prisoner’s dilemma
Round
π(d,d)
π(d,c)
π(c,d)
π(c,c)
Round
π(d,d)
π(d,c)
π(c,d)
π(c,c)
−5
−4
−3
−2
−1
100
350
0
150
31
100
250
0
200
200
300
0
250
32
50
350
0
150
300
450
0
350
33
150
450
0
400
100
300
0
200
34
100
450
0
400
250
400
0
300
35
50
250
0
200
1
250
350
0
300
36
100
350
0
200
2
300
400
0
350
37
150
450
0
300
3
150
450
0
350
38
150
400
0
250
4
150
400
0
200
39
200
400
0
250
5
150
350
0
200
40
100
300
0
150
6
100
300
0
250
41
50
450
0
100
7
50
300
0
150
42
50
300
0
200
8
150
350
0
300
43
200
400
0
350
9
100
450
0
350
44
200
350
0
250
10
250
400
0
350
45
50
350
0
250
11
50
200
0
150
46
100
400
0
300
12
150
450
0
250
47
200
450
0
300
13
150
250
0
200
48
100
350
0
300
14
50
350
0
100
49
50
450
0
250
15
100
350
0
250
50
100
400
0
250
16
250
450
0
350
51
150
400
0
300
17
250
450
0
300
52
100
400
0
150
18
350
450
0
400
53
100
450
0
200
19
100
400
0
200
54
50
450
0
150
20
150
400
0
350
55
50
250
0
150
21
50
400
0
250
56
100
350
0
150
22
150
300
0
200
57
200
300
0
250
23
150
350
0
250
58
300
450
0
350
24
50
400
0
350
59
100
300
0
200
25
300
450
0
400
60
250
400
0
300
26
150
450
0
200
27
50
450
0
400
28
150
300
0
250
29
50
350
0
200
30
50
300
0
100
Notes: Payoffs in Chilean pesos (CLP). Rounds
As of May 1st, 2010, 1 CLP = 0.0019 USD.
−5 to −1 are practice only.
Reciprocity and trust: Personality psychology meets behavioral economics
13
The probability that subject i chooses strategy s in round j is given by the following expression:
exp(λ E[uij (s, β)])
,
x∈S exp(λ E[uij (x, β)])
qij (s) = P
(21)
where
E[uij (s, β)] =

h
i
T −
T −

µ
(τ)π
(c,
c)
+
(1
−
µ
(τ))
(1
+
R
ρ
)π
(c,
d)
−
R
ρ
π
(d,
c)
if s = UC,

ij
j
ij
j
j
i
i



µij (τ)πj (c, c) + (1 − µij (τ)) πj (d, d)
if s = CC,


h
i


µ (τ) (1 − RT ρ+ )π (d, c) + RT ρ+ π (c, d) + (1 − µ (τ)) π (d, d) if s = DU,
ij
j
j
ij
j
i
i
and
µij (τ) =
pj exp(TT
i τ)
.
1 − pj + pj exp(TT
i τ)
(22)
(23)
The above equations are instances of equations (15)–(19). Variables Ri and Ti are subject i’s
vectors of personality traits, as measured by the reciprocity/trust psychometric questionnaire.
These scores are standardized, so that they have zero mean and unitary variance. Variable pj
is the empirical probability that the first mover cooperates blindly in round j. We define pj as
follows:
pj =
Mj
N
(24)
Where N is the number of subjects that participated in the experiment, and Mj is the number
of subjects that chose to cooperate blindly in round j.
5 Results
5.1 Exploratory analysis
The empirical distributions of personality traits, as measured by the reciprocity/trust psychometric questionnaire, are displayed in Figure 2.1 These distributions closely resemble those reported
by Dohmen et al. (2008). Most subjects obtained high scores in the positive reciprocity trait and
low scores in the negative reciprocity trait. The distribution of the trust trait is more symmetric
but slightly inclined to the left. Table 3 shows the correlations between the three scores. Positive
and negative reciprocity do not correlate with each other, while trust correlates positively with
positive reciprocity, and negatively with negative reciprocity.
The dynamics of cooperation in the sequential prisoner’s dilemma is summarized in Figure
3. The figure shows the fraction of subjects who chose a particular strategy by round of play.
1 The database with the results of the psychometric test and the prisoner’s dilemma experiment can be downloaded from here: https://mega.co.nz/#!1ZVUyRSS!UhYhUHrOLT5l9va2hmZshQ qzRYKRuhDHIhQ49I1nrU
Ricardo Andrés Guzmán et al.
0,3
0,3
0,2
0,2
0,2
0,1
0,0
Density
0,3
Density
Density
14
0,1
0,0
-3,7
-2,5 -1,2 0,0
1,2
Positive reciprocity trait
0,1
0,0
-1,2 -0,6 0,1 0,8 1,5 2,2 2,9
Negative reciprocity trait
-2,9 -2,1 -1,3 -0,4 0,4 1,2 2,0
Trust trait
Fig. 2: Empirical distribution of personality traits among the subjects.
Table 3: Correlations matrix of personality traits
Positive
reciprocity
Positive reciprocity
Negative reciprocity
Trust
Negative
reciprocity
1.00
0.07
0.16*
1.00
-0.36*
Trust
1.00
* Significant at the 5% level.
Table 4: Overall distribution of strategies
Role
Strategy
1st mover
Cooperate blindly
Defect blindly
Probability
0.31
0.69
2nd mover
Cooperate unconditionally
Cooperate conditionally
Defect unconditionally
0.02
0.47
0.51
Observe that all types of cooperative strategies decline throughout the game. This a typical
result in cooperative dilemma experiments (Ledyard 1995). Averaging over subjects and rounds,
we get the overall distribution of strategies. This is shown in Table 4.
What effects do incentives have on the second movers’ strategy choices? We specify incentives
as follows:
temptation = πdc − πcc ,
risk = πdd − πcd ,
reward = πcc − πdd .
Temptation is what what the second mover gains by defecting rather than cooperating when the
first mover cooperates. Risk is what the second mover loses by cooperating rather than defecting
when the first mover defects. Reward is what both players gain by cooperating together rather
than defecting together. Figure 4 shows the effects of incentives on the second movers’ strategy
choices. Observe that a higher temptation reduces unconditional and conditional cooperation,
y = −0.0015x + 0.36
R² = 0.04
60%
40%
20%
0%
1
Fraction of the subjects who
cooperated conditionally
Fraction of the subjects who
cooperated unconditionally
80%
11
21
31
Round
41
80%
60%
40%
y = −0.0038x + 0.58
R² = 0.38
20%
0%
1
11
21
31
Round
41
60%
40%
y = −0.0005x + 0.03
R² = 0.50
20%
0%
1
51
15
80%
51
Fraction of the subjects who
defected unconditionally
Fraction of the subjects who
cooperated blindly
Reciprocity and trust: Personality psychology meets behavioral economics
11
21
31
Round
41
51
80%
60%
40%
y = 0.0043x + 0.38
R² = 0.43
20%
0%
1
11
21
31
Round
41
51
Fig. 3: Fraction of the 212 subjects who chose a particular strategy by round of play. The top
left panel represents the choices of first movers: cooperate blindly (vs. defect blindly). The
other panels represent the choices of second movers: cooperate unconditionally, cooperate
conditionally, or defect unconditionally. All subjects played both roles —first and second
mover— in all rounds of play.
and increases unconditional defection. Risk, on the other hand, reduces only unconditional cooperation, albeit weakly. Finally, reward increases unconditional and conditional cooperation, and
reduces unconditional defection.
Figure 5 shows the effects of personality on the behavior of second movers. As can be seen in
the figure, positive reciprocity, negative reciprocity, and trust have a strong effect on the second
movers’ strategic choices.
5.2 Estimation of the model and hypotheses testing
Table 5 presents the maximum-likelihood estimates of the parameters of the model.2 Replacing
the estimated values into equations (2), (3), and (13) we can express the reciprocal preferences
2 To calculate the standard errors, p-values, and confidence intervals we used a semi-parametric bootstrapping
method. Each iteration consisted of three steps. First, we resampled the 212 subjects, with replacement (a subject
is a tuple of three elements: a positive reciprocity trait, a negative reciprocity trait, and a trust trait). Second, we
Ricardo Andrés Guzmán et al.
y = -4E-05x + 0.022
R² = 0.05
4%
2%
0%
0
100 200 300
Temptation (CLP)
4%
2%
0%
0
100 200 300
Risk (CLP)
0%
0
200
Temptation (CLP)
0%
0
100 200 300
Risk (CLP)
0%
0
100 200 300
Temptation (CLP)
400
400
50%
25%
y = 0.0011x + 0.39
R² = 0.45
100 200 300
Reward (CLP)
75%
50%
25%
400
y = 0.0008x + 0.37
R² = 0.32
0
Fraction of the subjects who
defected unconditionally
50%
100 200 300
Reward (CLP)
0%
400
75%
Fraction of the subjects who
defected unconditionally
75%
0%
25%
y = 1E-05x + 0.47
R² = 0.00
400
2%
50%
25%
y = -0.001x + 0.59
R² = 0.47
4%
75%
50%
25%
y = 5E-05x + 0.011
R² = 0.09
0
Fraction of the subjects who
cooperated conditionally
50%
6%
400
75%
Fraction of the subjects who
cooperated conditionally
Fraction of the subjects who
cooperated conditionally
y = -3E-05x + 0.021
R² = 0.03
400
75%
Fraction of the subjects who
defected unconditionally
6%
Fraction of the subjects who
cooperated unconditionally
6%
Fraction of the subjects who
cooperated unconditionally
Fraction of the subjects who
cooperated unconditionally
16
25%
y = 2E-05x + 0.51
R² = 0.00
0%
0
100 200 300
Risk (CLP)
400
y = -0.0009x + 0.62
R² = 0.32
0%
0
100 200 300
Reward (CLP)
400
Fig. 4: Effects of incentives on the second movers’ strategy choices. Temptation = πdc − πcc ,
risk = πdd − πcd , reward = πcc − πdd .
and the trust coefficient as functions of the reciprocity traits:
r+ = 0.27 + 0.06R+ − 0.12R− ,
(25)
r− = 1.05 + 0.15R− ,
(26)
t = 0.20T.
(27)
These equations only include the values statistically significant at the 10% level. The results
confirm hypotheses 1, 2, 4, and 5, while hypothesis 3 is only partially confirmed (equality (9) is
falsified by the data).
simulated the model using the resampled subjects, using equations (15)–(19) and the parameters estimated from
the actual sample. Third, we used the bootstraped sample to re-estimate the parameters of the model.
0,0%
2,5%
0,0%
-4
-2
0
2
Positive reciprocity score
100%
y = 0.026x + 0.47
R² = 0.15
75%
50%
25%
0%
75%
75%
50%
25%
0%
-4
-2
0
2
Positive reciprocity score
0,0%
-3
25%
0%
75%
-1,5
0
1,5
Trust score
3
y = 0.0191x + 0.47
R² = 0.09
75%
50%
25%
0%
-2
0
2
4
Negative reciprocity score
Fraction of the subjects who
defected conditionally
Fraction of the subjects who
defected conditionally
y = -0.0446x + 0.47
R² = 0.52
100%
y = -0.026x + 0.51
R² = 0.14
2,5%
y = 0.0049x + 0.017
R² = 0.25
100%
50%
-4
-2
0
2
Positive reciprocity score
100%
5,0%
-2
0
2
4
Negative reciprocity score
Fraction of the subjects who
cooperated conditionally
Fraction of the subjects who
cooperated conditionally
100%
Fraction of the subjects who
cooperated unconditionally
2,5%
y = -0.0071x + 0.017
R² = 0.54
Fraction of the subjects who
cooperated conditionally
y = 0.0003x + 0.017
R² = 0.00
5,0%
17
-3
-1,5
0
1,5
Trust score
3
100%
y = 0.0517x + 0.51
R² = 0.57
50%
25%
0%
Fraction of the subjects who
defected conditionally
5,0%
Fraction of the subjects who
cooperated unconditionally
Fraction of the subjects who
cooperated unconditionally
Reciprocity and trust: Personality psychology meets behavioral economics
-2
0
2
4
Negative reciprocity score
y = 0.0191x + 0.47
R² = 0.09
75%
50%
25%
0%
-3
-1,5
0
1,5
Trust score
3
Fig. 5: Effects of personality on the second movers’strategy choices. The areas of the circles
correspond to the number of subjects who got the same score on the personality trait.
In summary:
−
1. The average second mover’s utility is strictly increasing in his payoff (ρ+
0 < 1, ρ0 > −1)
2. The average second mover is a positive reciprocator (ρ+
0 ∈ (0, 1]) and negative reciprocator
(ρ−
0 > 0)
3. The positive reciprocal preference is increasing in the positive reciprocity trait (ρ+
1 > 0), and
decreasing the negative reciprocity trait (ρ+
2 < 0).
3
4. The negative reciprocal preference is increasing in the negative reciprocity trait (ρ−
2 > 0),
and does not depend on the positive reciprocity trait (ρ−
1 = 0).
5. The trust coefficient is increasing in the trust trait (τ1 > 0).
3
This relation is marginally significant (p-value = 0.1).
18
Ricardo Andrés Guzmán et al.
Table 5: Maximum-likelihood estimates of the parameters of the model
Parameter
Coeff.
Std. err.
p-value
0.27
0.02
0.00
[90% conf. inter.]
[95% conf. inter.]
Pos. reciprocal preference
Constant (ρ+
0 )
Pos. reciprocity trait (ρ+
1 )
Neg. reciprocity trait (ρ+
2 )
0.24
0.30
0.24
0.30
0.06
0.02
0.00
0.04
0.09
0.03
0.10
-0.12
0.03
0.00
-0.17
-0.08
-0.19
-0.07
Constant (ρ−
0 )
1.05
0.26
0.00
0.73
1.57
0.68
1.70
Pos. reciprocity trait (ρ−
1 )
Neg. reciprocity trait (ρ−
2 )
0.04
0.04
0.22
-0.02
0.11
-0.03
0.12
0.15
0.10
0.10
0.00
0.32
-0.03
0.36
Constant (τ0 )
0.09
0.16
0.60
-0.18
0.36
-0.22
0.42
Trust trait (τ1 )
0.20
0.08
0.01
0.06
0.34
0.04
0.37
0.0109
0.0014
0.00
0.0089
0.0132
0.0081
0.0139
Neg. reciprocal preference
Trust coefficient
Rationality parameter (λ)
Note: Bootstrapped standard errors, p-values, and confidence intervals (10.000 draws).
6 Conclusion
Even though the domain of our synthetic model is limited to the current experimental design,
the empirical validity of the model is relevant to both behavioral economics and personality
psychology. From the point of view of behavioral economics, the synthetic model is a small step
toward a theory of heterogeneous preferences and beliefs, which should be explained (at least in
part) as a result of personality differences. This is important, because a theory of heterogeneous
preferences and beliefs is an essential ingredient of any full-fledged model of human behavior.
From the point of view of personality psychology, the empirical validity of the synthetic model
indicates that economic theory can be used to understand how the behavioral manifestations
of personality are affected by the situation; specifically, by material incentives. Ultimately, the
results of this study suggest that a synthesis between behavioral economics and personality
psychology is possible and potentially fruitful.
Acknowledgments
For their valuable comments and suggestions, we thank Leda Cosmides, James C. Cox, Giuseppe
Attanasi, Aaron Lukaszewski, and Carlos Rodrı́guez-Sickert. Marı́a Ignacia Rivera and Eric
González provided research assistance. This research was conducted with the financial support
of Fondecyt grant #1120387, and Proyecto Anillo SOC1101.
Reciprocity and trust: Personality psychology meets behavioral economics
19
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