=Paper=
{{Paper
|id=Vol-1627/paper7
|storemode=property
|title=Gift Ratios in Laboratory Experiments
|pdfUrl=https://ceur-ws.org/Vol-1627/paper7.pdf
|volume=Vol-1627
|authors=Rustam Tagiew,Dmitry I. Ignatov
|dblpUrl=https://dblp.org/rec/conf/cla/TagiewI16
}}
==Gift Ratios in Laboratory Experiments==
https://ceur-ws.org/Vol-1627/paper7.pdf
Gift Ratios in Laboratory Experiments
Rustam Tagiew1 and Dmitry I. Ignatov2
1 POLAREZ ENGINEERING, Dresden, Germany,
Alumni of TU Freiberg and Uni Bielefeld, Germany
rustam.tagiew@polarez.com, http://www.polarez.com
2 National Research University Higher School of Economics, Moscow, Russia
dignatov@hse.ru, https://www.hse.ru/en/staff/dima
Abstract. This paper presents statistics of a controlled laboratory gift-exchange-
game experiment. These numbers can be used for assumptions about human be-
havior in analysis of noisy web data. The experiment was described in ‘The Im-
pact of Social Comparisons on Reciprocity’ by Gächter et al. 2012. As already
shown in relevant literature from experimental economics, human decisions de-
viate from rational payoff maximization. The average gift rate was 31%. Gift rate
was under no conditions zero. Further, we derive some additional findings and
calculate their significance.
1 Introduction
As our experience shows [1], extraction of knowledge from noisy industrial datasets
requires reasonable assumptions. Data analysis results extracted from clean data of lab-
oratory experiments can help to create these assumptions. Market leaders in Big Data,
as Microsoft, Facebook, and Google, have already realized the importance of experi-
mental economics know-how for their business [2][3][4].
Before vast data and computational power were available, classical economists used
game theory to predict outcomes of human interactions. People were assumed to be in-
telligent and autonomous, and to act pursuant to their existing preferences. It is impor-
tant to underline that game theory is a mathematical discipline, whose task was never
to define human preferences, but to calculate based on their definition. A preference
is an order on outcomes of an interaction. One can be regarded as rational, if one al-
ways makes decisions, whose execution has referred to subjective estimation the most
preferred consequences [5,6]. The level of intelligence determines the correctness of
subjective estimation. Beyond justifying own decisions, rationality is a base for predic-
tions of other people’s decisions. If the concept of rationality is satisfied, and applied
mutually, and even recursively in a human interaction, then the interaction is called
strategic. Game is a notion for the formal structure of a concrete strategic interaction
[7].
A definition of a game consists of a number of players, their preferences, their pos-
sible actions and the information available for the actions. A payoff function can replace
the preferences under assumed payoff maximization. The payoff function defines each
player’s outcome depending on his actions, other players’ actions and random events
in the environment. The game-theoretic solution of a game is a prediction about the
Gift Ratios in Laboratory Experiments 83
behavior of the players also known as an equilibrium. The basis for an equilibrium is
the assumption of rationality. Deviating from an equilibrium is outside of rationality,
because it does not maximize the payoff according to the formal definition. There are
games, which have no equilibria. At least one mixed strategies equilibrium is guaran-
teed in finite games [8].
In common language, the notion of game is used for board games or video games.
In game-theoretic literature, it is extended to all social, economical and pugnacious in-
teractions among humans. A war can be simplified as a board game. Some board games
were even developed to train people, like Prussian army war game ‘Kriegspiel Chess’
[9] for their officers. We like it to train in order to perform better in games [10]. In
most cases, common human behavior in games deviates from game-theoretic predic-
tions [11,12]. One can say without any doubt that if a human player is trained in a
concrete game, he will perform close to equilibrium. But, a chess master is not neces-
sarily a good poker player and vice versa. On the other side, a game-theorist can find a
way to compute an equilibrium for a game, but it does not make a successful player out
of him. There are many games we can play; for most of them, we are not trained. That is
why it is more important to investigate our behavior while playing general games than
playing a concrete game on expert level.
Although general human preferences are a subject of philosophical discussions [13],
game theory assumes that they can be captured as required for modeling rationality. Re-
garding people as rational agents is disputed at least in psychology, where even a scien-
tifically accessible argumentation exposes the existence of stable and consistent human
preferences as a myth [14]. The problems of human rationality can not be explained
by bounded cognitive abilities only. ‘... people argue that it is worth spending billions
of pounds to improve the safety of the rail system. However, the same people habitu-
ally travel by car rather than by train, even though traveling by car is approximately 30
times more dangerous than by train!’[15, p.527–530] Since the last six decades never-
theless, the common scientific standards for econometric experiments are that subjects’
preferences over outcomes can be insured by paying differing amounts of money [16].
However, insuring preferences by money is criticized by tossing the term ‘Homo Eco-
nomicus’ as well.
The ability of modeling other people’s rationality and reasoning as well corresponds
with the psychological term ‘Theory of Mind’ [17], which lacks almost only in the cases
of autism. For experimental economics, subjects as well as researchers, who both are
supposed to be non-autistic people, may fail in modeling of others’ minds anyway.
In Wason task at least, subjects’ reasoning does not match the researchers’ one [18].
Human rationality is not restricted to capability for science-grade logical reasoning –
rational people may use no logic at all [19]. However, people also make serious mis-
takes in the calculus of probabilities [20]. Even in mixed strategy games, where random
behavior is of a huge advantage, the required sequence of random decisions can not
be properly generated by people [21]. Due to bounded cognitive abilities, every human
‘random’ decision depends on previous ones and is predictable in this way. In ultima-
tum games [12, S. 43ff], the former economists’ misconception of human preferences
is revealed – people’s minds value fairness additionally to personal enrichment. Our
minds originated from the time, when private property had not been invented and social
84 Rustam Tagiew and Dmitry Ignatov
values like fairness were essential for survival.
From the view point of data scientists fascinated by human behavior, the sizes of
datasets originated from social networks predominate the ones from experimental eco-
nomics by orders of magnitude [12]. Nevertheless, analyzing data from experimental
economics has the same importance for understanding human psychology as studying
Escherichia for understanding human physiology. Data from experimental economics
has the advantage of originating from simple and controlled human interactions.
In current experimental economics, the models are first constructed by philosoph-
ical plausibility considerations and then are claimed to fit the data. In this work, we
reverse the order of common research in experimental economics. We follow the slo-
gan ‘existence precedes essence’ – the philosophical plausibility considerations follow
after the correlations and regularities are found. For these needs, we analyze the dataset
of the paper “The Impact of Social Comparisons on Reciprocity” by Gächter et al. [22].
The only assumption about human behavior is its determinism.
The next section summarizes related work on data mining approaches and econom-
ical models. Then, the experiment setup and the gathered data are introduced. Before
extracting rules of behavior, we explain the reasons for the assumption of determinism.
We also explain conceptual problems of using linear model on this data. The results
and their interpretations follow afterwards. Then, a section is devoted to p-hacking. A
suggestion for more efficient research on human behavior is made in future work. Sum-
mary and discussion conclude this paper.
2 Related Work
A similar approach is already explored on three datasets – a zero-sum game of mixed
strategies, an ultimatum game and repeated social guessing game [23,24]. For these
datasets, extracted deterministic regularities outperformed state-of-art models. It was
shown that some regularities can be easily verbalized, what underlines their plausibil-
ity.
A very comprehensive gathering of works in experimental psychology and eco-
nomics on human behavior in general games can be found in [25]. Quantal response
equilibrium became popular as a model for deviations from equilibria [26]. It is a
parametrized shift between mixed strategies equilibrium and an equal distribution. The
basic idea for quantal response equilibrium is the concept of trembling hand – people
make mistakes with certain probability. Unfortunately, the Akaike information criterion
[27] is rarely calculated to judge the trade-off between fit quality and model complexity
[28]. Another popular model is the linear regression. It is used in the original paper to
model the dataset [22]. For linear regression, data is translated into real numbers.
3 Gift-Exchange-Game
Since Akerloff and Yellen published their leading work [29] on unemployment, gift-
exchange-games (GEG) became standard for modeling labor relations. Such a game
Gift Ratios in Laboratory Experiments 85
involves at least two players – an ‘employer’ and an ‘employee’. The ‘employer’ has to
decide first, whether to award a higher salary or not. Then, the ‘employee’ has to decide,
whether to put extra effort or not. Unfortunately, the experiment conducted by Gächter
et al. did not implement a real-effort task. The ‘employee’ does not put real effort, but
can decide to make a gift, which reduces his/er own payoff. Nevertheless, this game
is not zero-sum. For what it’s worth, real-effort tasks are already established in exper-
imental economics – in works of Ariely e.g. [30]. Therefore, we refuse to draw any
inferences from the behavior in the experiment to the behavior in real labor relations.
The ‘employer’ is renamed to originator and ‘employee’ to follower. If the originator
and the follower are both only interested in maximizing their payoff in a pure monetary
case and it is a one-shot game, the actual gift exchange will not take place.
The experiment was conducted at University of Nottingham and consisted of one-
shot games, whereby no subject participated twice. The participants were 20 years old
in average and of both genders. Every one-shot game involves three players – one orig-
inator and two followers. The originator has the choice to award none, one or both
followers. The followers have four levels of rewarding (including non-rewarding) the
originator. In the original game description, the originator and every follower have to
give at least a minimum gift, which we denote non-gift for simplicity. At the beginning,
the originator gets £8.3 and every follower gets £11.1. The additional payoff of the
originator is the sum of margins from gift exchange with both followers. The additional
payoff of every follower is the gift of the originator minus reduction through own gifts.
The originator can give a fixed amount of £1.6 to a follower. A follower can give £1, £2
or £3, whereby his/er payoff reduces by £0.5, £1 or £1.5 accordingly.
We split the 3-players game into two 2-players games. Fig.1 shows the 2-players
game between an originator and a follower in extensive form. Extensive form is known
in AI as game tree. The originator has to decide for two of such 2-players games. After
the originator makes his choice, the followers make their choices either sequentially
or simultaneously. Every follower can observe both of originators’ decisions. In the
sequential case, first follower’s decision can be seen by the second follower. Besides
mutual visibility, both 2-players games are independent. Adding both games, the origi-
nator’s total payoff ranges between £5.1 and £14.3. The follower’s total payoff ranges
between £9.6 and £12.7.
4 Dataset
123 subjects participated in the game – 84 for the sequential case and 39 for the simul-
taneous case. 1233 = 41 originators have made 41 × 2 = 82 decisions – two 2-players
games per originator. The follower were asked to submit their decisions for every pos-
sible combination of others’ observable decisions. There are 4 decision combinations
for an originator. First followers in the sequential case submitted 4 ∗ 84
3 = 112 and all
followers in the simultaneous case submitted 4 ∗ 2 ∗ 39
3 = 104 decisions. Second follow-
84
ers in the sequential case submitted 4 ∗ 4 ∗ 3 = 448 decisions. Therefore, we have a
dataset of total 746 human decisions.
86 Rustam Tagiew and Dmitry Ignatov
Originator
0
Follower
0 3 1.6
1 2
(0, 0) (3, −1.5)
(1, −.5) (2, −1) Follower
0 3
1 2
(−1.6, 1.6) (1.4, .1)
(−.6, 1.1) (.4, .6)
Fig. 1. Experimental non-zero-sum 2-players GEG in extensive form. (Originator’s payoff, Fol-
lower’s payoff) – payoffs are in £. Payoff maximizing equilibrium is marked by dashed lines.
5 Assumption of determinism
Modeling human behavior outside of game playing with human subjects should not be
confused with prediction algorithms of artificial players. Quite the contrary, artificial
players can manipulate the predictability of human subjects by own behavior. For in-
stance, an artificial player, which always throws ‘stone’ in roshambo, would success at
predicting a human opponent always throwing ‘paper’ in reaction. Otherwise, if an arti-
ficial player maximizes its payoff based on opponent modeling, it would face a change
in human behavior and have to deal with it. This case is more complex than a spectator
prediction model for an ‘only-humans’ interaction. This work is restricted on modeling
behavior without participating.
Human behavior can be modeled as either deterministic or non-deterministic. Al-
though human subjects fail at generating truly random sequences as demanded by mixed
strategies equilibrium, non-deterministic models are especially used in case of artificial
players in order to handle uncertainties.
‘Specifically, people are poor at being random and poor at learning optimal move
probabilities because they are instead trying to detect and exploit sequential dependen-
cies. ... After all, even if people don’t process game information in the manner suggested
by the game theory player model, it may still be the case that across time and across in-
dividuals, human game playing can legitimately be viewed as (pseudo) randomly emit-
ting moves according to certain probabilities.’ [31] In the addressed case of spectator
prediction models, non-deterministic view can be regarded as too shallow, because de-
terministic models allow much more exact predictions. Non-deterministic models are
only useful in cases, where a proper clarification of uncertainties is either impossible or
costly. To remind, deterministic models should not be considered to obligatory have a
Gift Ratios in Laboratory Experiments 87
formal logic shape.
6 Nominal, Ordinal or Numeric
The usage of right data types is essential for correct data analysis. There are basically
three categories, in which variables can be classified – nominal, ordinal and numeric.
Nominal variables assume values from a finite set, which has no order. Ordinal variables
are like nominals plus ordering relationship over the set of values. Numeric variables
assume real numbers R as values. Ordinal values can be projected into numeric under
assumption about their distribution over the number axis. In contrast, nominal values
can not.
Some variables, which impact human actions, are actions of other players. Since
presuming human preferences over the outcomes has no base, an ordering relationship
over the actions can not be presumed as well. In the addressed problem, all variables
impacting human actions are actions of others. Preferences over outcomes in the earlier
described GEG can not be presumed. For instance, the outcomes (.4, .6) and (1.4, .1)
(Fig.1) are the total payoffs (£8.7, £11.7) and (£9.7, £11.2). An egoistic follower would
prefer the first and altruistic one the second. Since the variables have to be nominal and
not even ordinal, they can not be projected into real numbers. An application of a linear
model as in the original paper [22] becomes therefore nonsense for this data.
7 Results
Originator’s both decisions are nominal or rather boolean – it is either a gift or not. In av-
erage, originators gift in 36.6% of samples. We calculate Kappa [32,33] to measure the
inter-rater agreement between these two decisions. Having zero Kappa as null hypothe-
sis, the significance of the measured Kappa can be calculated. Tab.1 displays significant
fair agreement between originator’s both decisions in the sequential case. There is no
significant agreement between them in the simultaneous case. Unfortunately, the data is
too marginal and Fisher’s test [34] does not show any significant difference between the
frequencies in both cases – p-value is 0.4686. We can at least claim that both decisions
are dependent in the sequential case.
Tab.2 shows absolute statistics for the follower’s decisions, which did not observe
another follower. Besides own received gift, there is the gift received by the other fol-
lower, which might have an impact on the observing follower’s decision. If no own gift
is received in the simultaneous case, Fisher’s test results a p-value of 0.0496 for gifting
>£0 depending on whether or not the other follower received a gift. Receiving less than
the other follower is therefore significantly reciprocated in the simultaneous case only.
The significance of this result is thoroughly discussed in section 8. In the sequential
case, there is no significant difference between decision frequencies depending on the
other’s received gift. Obviously, the order between the follower delivers a reason for an
unequal treatment.
88 Rustam Tagiew and Dmitry Ignatov
Table 1. Originator’s two decisions – absolute statistics and agreements.
Sequential Simultaneous Sum
Gifts for 1st 9 6 15
Gifts for 2nd 10 5 15
All samples 28 13 41
Kappa .4432 .2169 .3692
p-value .017 .22 .014
Table 2. Follower’s decision without observing another follower’s decision – absolute statistics.
Sequential Simultaneous
Own gift £0 £1 £2 £3 £0 £1 £2 £3
Received gifts
Own Other’s
£0 £0 21 6 1 0 19 7 0 0
£0 £1.6 21 6 1 0 25 0 1 0
£1.6 £0 13 6 5 4 16 6 4 0
£1.6 £1.6 13 6 4 5 16 3 4 3
Tab.3 lists agreements as well as their significances between subsets of own deci-
sions and observed decisions. The subsets of own decisions are defined by thresholds on
gift size. We use thresholds to define subsets, because based on decreasing frequencies
by raising gift size (Tab.2), an order on the gift decisions can be derived. One can see
that only own received gift has a significant influence on own decision in sequential as
well as in simultaneous cases. Since only one variable has influence on the decision, the
deterministic model is trivial – gift >£0 in the sequential case having received a gift,
non-gift anywhere else.
As Fig.2 shows, non-gift covers ≥ 50% of decisions for the second follower for all
possible combinations of input variables and 71.2% in average. One can of cause as-
sume that some hidden variables influence the gift decision. Since we do not see these
variables, we can not build a useful valid deterministic model – none can be better than
the null hypothesis suggesting non-gift everywhere. We restrict the analysis to agree-
ments between the decision and the three observed variables.
Tab.4 shows the agreements between subsets of the second follower’s decisions and
the decisions of the originator – none of them is significant. It also shows the agreement
between the decisions of the first and the second follower, whereby correspondence be-
tween the values’ sets of both variables is assumed. This agreement is not significant.
Therefore, the value sets of both variables have to be transformed. Tab.5 shows agree-
ments between both variables transformed to booleans in different combinations. The
highest agreement and the lowest p-value are achieved for the first follower’s gift >£1
Gift Ratios in Laboratory Experiments 89
Table 3. Follower’s decision without observing another follower’s decision – agreements with
originator’s decisions.
.......Sequential....... Simultaneous
Kappa p-value Kappa p-value
Own gift ... ... vs. received gift
>£0 .2857 .0012 .2308 .0093
>£1 .2857 .0012 .1923 .0249
>£2 .1607 .045 .0577 .2781
... vs. other’s received gift
>£0 0 .5
<£1 .1154 .1197
>£1 0 .5 .0769 .2164
>£2 .0179 .4251 .0577 .2781
and the second one’s >£0. Once the first follower is extra generous, the second one is
also driven to gift the originator.
To summarize, the frequency of non-gift is 63.4% for the originator, 60.7% for the
first sequential follower, 73% for the simultaneous follower and 71.2% for the second
sequential follower. According to Fisher test, none of these frequencies significantly
deviates from the rest. The average non-gift frequency is 69%.
8 On p-hacking
It is not a secret that p-values closely under 0.05 cause suspicion about the scientific
methods used in research [35]. Although p-value was never thought to be an objective
criterion for proof or disproof of a hypothesis, many researchers misunderstand it and
conduct the so called ’p-hacking’ on the data to archive significant results.
The results achieved through p-hacking might not be reproducible, since the a-priori
probabilities of the hypotheses have to be incorporated as well. For instance, if the hy-
pothesis is a long shot and has an a-priori probability of 5%, a p-value of 0.01 raises the
chance of its validity to only 30%. The more hypotheses are tested on p-value, the higher
the probability to achieve a p-value under 0.05. Obviously, the difference between long
shots and good bets has to be derived from the researcher’s expert knowledge, which
is known to be absent in the case of an pure data scientist analyzing human data. Here,
we suggest the data scientist to be ’agnostic’ and use some background knowledge to
advocate the result.
During the data analysis in this paper, we got a p-value of 0.0496 for the hypoth-
esis that an unfairly treated simultaneous follower negatively reciprocates. Using the
background knowledge about human reaction to unfairness [36], we can assume that it
is a good bet. If the a-priori probability for a good bet is assumed to be about 90%, a
90 Rustam Tagiew and Dmitry Ignatov
28
3
26 2
1
24 0
22 50%
20
18
Absolute statistics
16
14
12
10
8
6
4
2
0
NN0
NY0
YN0
YY0
NN1
NY1
YN1
YY1
NN2
NY2
YN2
YY2
NN3
NY3
YN3
YY3
Fig. 2. Choice of the second follower – absolute statistics depending on other players’ decisions
encoded on x-axis as: other follower’s received, own received and other follower’s given. N is £0
and Y £1.6.
p-value of 0.05% raises its chance of validity to 96%.
9 Future work
During the work on this paper, we confronted the time consuming requesting, selection
and reformatting of data. Unfortunately, there is no online portal, where most of the
datasets are offered in a common format. This is an issue, which we will address in the
future. Like in the field of bioinformatics, common formats are an important part of an
interdisciplinary research infrastructure and are needed to accelerate the progress [37].
As for methodological aspects of Machine Learning in the context of Experimental
Economics, we would like to use the advanced pattern mining techniques for economic
game data analyses. For example, in papers [38,39] was made an attempt to use sequen-
tial patterns and similarity dependencies on pattern structures for video game players’
behavior analysis, in particular sequential attribute dependencies might be a tool of
choice. We will try to apply sequential pattern mining in a supervised task, where the
outcome of a game (or a turn) is a target attribute [40,41] to see which patterns better
generalize the user behavior. These experiments are able not only to broad the tools of
experimental economics, but also help to reveal potentially new knowledge of human
behavior in games based on sequential pattern description.
Gift Ratios in Laboratory Experiments 91
Table 4. Second follower’s decision – agreements.
Sequential case
Kappa p-value
Own gift ... ... vs. received gift
>£0 .0223 .3183
>£1 .0223 .3183
>£2 .0134 .3884
... vs. other’s received gift
>£0 .0045 .4624
>£1 .0402 .1975
>£2 .0134 .3884
... vs. other’s gift
.0446 .0509
Table 5. First and second follower’s decision – agreements between subsets.
1st follower >£0 >£1 >£2
Kappa p-value Kappa p-value Kappa p-value
2nd follower
>£0 .1123 .0016 .2634 1.238e − 8 .1445 .0068
>£1 .0564 .0365 .1563 .0005 .1345 .029
>£2 .026 .1826 .0759 .0541 .0456 .2789
10 Conclusion
First of all, the average non-gift frequency is only 69% in the studied one shot GEG.
These are far away from the 100%, which an egoistic payoff maximization assumption
would predict. But, it is also over 50% in almost all cases. There, it is impossible to
create valid nontrivial deterministic models of human behavior without having access
to the hidden variables, which determine the choice. Only if the first follower receives
a gift in the sequential case, the frequency of gifts goes slightly over 50%.
Although first follower’s decision depends only on his received gift and second fol-
lower’s decision does not depend on originators’ decisions at all, originators’ decisions
are interdependent in the sequential case. The order between the players obviously de-
livers a reason for the first follower to not mind differences in gifts. Having no order in
the simultaneous case leads to significant negative reciprocation of receiving less than
the second follower.
A curious finding is that not minimal but extra generosity is ’contagious’ for the
followers. Second follower reacts only on the first follower being extra generous and
92 Rustam Tagiew and Dmitry Ignatov
with normal generosity.
Acknowledgment The authors would like to thank Martin Sefton for the friendly reply
and the transfer of data. We also thank the people, who provided the Weka library, for
their wonderful work, as well as Minato Nakazawa for the fmsb package.
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