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Journal ArticleDOI

Conditional cooperation: Type stability across games

01 Mar 2020-Economics Letters (North-Holland)-Vol. 188, pp 108941

Abstract: To classify cooperation types, a sequential prisoner’s dilemma and a one-shot public goods game are convenient experimental setups. We explore the within subject stability of cooperation preferences in these two games. We find that the prisoner’s dilemma performs well in identifying conditional cooperators while it is only an imperfect tool for identifying selfish types in the public goods game.
Topics: Public goods game (62%), Dilemma (51%)

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BGPE Discussion Paper
No. 186
Conditional cooperation:
Type stability across games
Michael Eichenseer
Johannes Moser
June 2019
ISSN 1863-5733
Editor: Prof. Regina T. Riphahn, Ph.D.
Friedrich-Alexander-Universität Erlangen-Nürnberg
© Michael Eichenseer, Johannes Moser

Conditional cooperation:
Type stability across games
Michael Eichenseer
University of Regensburg
Johannes Moser
University of Regensburg
June 11, 2019
Abstract
In this paper, we use an experimental setup to classify cooperation types using
a sequential prisoner’s dilemma and a one shot sequential public goods game.
In these two games, we examine the within subject stability of cooperation
preferences. Our results suggest that subjects classified as conditional coop-
erators in the prisoner’s dilemma match others’ contributions in the public
goods game to a significantly larger degree compared to other types, which
indicates a substantial consistency. Regarding discrete behavioral types, we
find that the prisoner’s dilemma performs well in identifying conditional co-
operators while it is only an imperfect tool for identifying selfish types in the
public goods game.
JEL-Classification: C72, C91, H41
Keywords: conditional cooperation, public goods game, sequential prisoner’s dilemma,
discrete behavioral types
Eichenseer and Moser: University of Regensburg, Department of Economics, Universit¨atsstraße
31, 93040 Regensburg. Email: michael.eichenseer@ur.de; johannes.moser@ur.de. Michael
Eichenseer and Johannes Moser acknowledge funding by the International Doctoral Program
Evidence-Based Economics of the Elite Network of Bavaria. We would like to thank Wolfgang
Buchholz, Francesco Fallucchi, Moritz Janas, Michael Kosfeld, Andreas Roider, and Christian
Th¨oni for helpful comments. All errors remain our own.

1 Introduction
One of the main contributions of behavioral economics is to establish the behavioral
relevance of another type beyond the purely payoff-maximizing “homo oeconomi-
cus”, named “homo reciprocans”, who represents a large fraction of the population.
1
If a researcher needs to determine behavioral types of subjects in the lab, there are
essentially two methods available to him. On the one hand, he can use the method
introduced by Fischbacher, achter, and Fehr (2001) which relies on a conditional
contribution vector elicited by the strategy method in a one-shot public goods game
(FGF hereafter).
2
This method is typically based on a set of 22 questions.
3
On the
other hand, a simple sequential prisoner’s dilemma (SPD hereafter), for which only
three questions are sufficient, can be used for type classification as well (Miettinen,
Kosfeld, Fehr, and Weibull, 2017; Kosfeld, 2019; Eichenseer and Moser, 2019). For
a researcher, the question arises whether using the simpler method is sufficient for
type classification as it may save time and reduce cognitive load for the participants.
To the best of our knowledge, there exists no systematic comparison of classification
congruence between these two procedures.
Consequently, the aim of this paper is to assess the stability of classifications
across games thereby contributing to the literature on the within subject stability
of cooperation preferences (Blanco, Engelmann, and Normann, 2011; Volk, Th¨oni,
and Ruigrok, 2012). To this end, we compare the types assigned by SPD to those
assigned by FGF in its latest refinements (Fallucchi, Luccasen, and Turocy, 2018;
Th¨oni and Volk, 2018). The remainder of this paper will be as follows: Section 2
describes the experimental design and procedures. Section 3 presents and discusses
our results. Section 4 provides as short summary and concludes.
2 Design and procedures
2.1 Protocol
The experiment was conducted on Amazon Mechanical Turk (MTurk henceforth)
in December 2018 using a sample of MTurk experienced US residents. In total,
232 participants took part in the experiment earning $2.85 on average with an
average completion time of approximately 13 minutes. About half of the subjects
1
See, for example, Fehr and achter (2000), Dohmen, Falk, Huffman, and Sunde (2009), and
Kosfeld (2019).
2
This method is by now the most commonly used one and, for example, labeled as ‘P-
Experiment’ in Fischbacher and achter (2010).
3
As a second-mover, subjects are typically asked to specify their contribution conditional on the
other players’ average contribution for integers in the interval [0, 20]. This results in 21 questions
plus an unconditional contribution question for the role as first-mover.
1

(120) played SPD first, while the other half (112) was doing the FGF task first.
Subsequently, the participants completed a short questionnaire on age, gender, and
education. Instructions for the experiment can be found in Appendix A.
2.2 Sequential Prisoner’s Dilemma (SPD)
In the SPD we have two players, indexed by i = 1, 2. Each player can choose between
actions SEND (S) and KEEP (K). Choices are elicited by using the strategy method
such that Player 2 can condition his choice on the action of Player 1. Figure 1 depicts
the structure of the game in extensive form including the resulting final payoffs in
POINTS (worth $0.05 each). The social optimum is reached when Player 1 chooses
S and Player 2 responds with action S as well. However, maximizing their own
payoffs means that Player 2 will choose action K at both decision nodes and Player
1, who anticipates this behavior, chooses K at the beginning. This is the unique
subgame-perfect equilibrium of this game. Hence, the decision situation resembles
a sequential prisoner’s dilemma.
P1
P2
(20 , 20)
S
(0 , 30)
K
S
P2
(30 , 0)
S
(10 , 10)
K
K
Figure 1: Payoff structure of the sequential prisoner’s dilemma
All subjects state decisions for both being Player 1 and 2 (strategy method).
They are randomly allocated to one of these roles at the end of the experiment and
paid accordingly. The set of strategies, X
i
, in this game for Player 2 is given by X
i
=
{SS, KK, SK, KS}.
4
Based on the participants’ conditional second mover’s choices,
we can classify subjects as altruists (unconditional cooperators), conditional coop-
erators (cooperate only if the first-mover cooperates), free-riders (never cooperate),
and mismatchers (counteract the other player) as depicted in Table 1.
4
The first action is played when Player 1 chooses SEND and the second action is played when
Player 1 chooses KEEP.
2

Cooperation type Strategy
Conditional cooperator (CC) (SEND, KEEP )
Selfish (SF) (KEEP, KEEP )
Altruist (AL) (SEND, SEND)
Mismatcher (MM) (KEEP, SEND)
Table 1: Cooperation types in SPD
2.3 Sequential Public Goods Game (FGF)
For the conditional contributions task in FGF, we used an adapted version of the
procedure of Fischbacher, achter, and Fehr (2001). Four players, indexed by
i = 1, 2, 3, 4, play a sequential public goods game in which one player makes his
contribution after observing the other three players’ rounded average contribution
when they were moving simultaneously beforehand. The resulting payoff of player i
with initial endowment y
i
= 20 POINTS is given by:
π
i
= y
i
g
i
+ α
4
X
j=1
g
j
where g
i
[0, 20] denotes individual contributions and α = 0.4 is the marginal per
capita return (MPCR) of the public good. Choices are elicited by using the strategy
method such that every player i makes a choice both for being one of the three first-
movers (unconditional contribution) and being a second-mover (contribution table).
As a second-mover, subjects condition their contribution g
i
on the average contribu-
tion (rounded to the next integer) of the first-movers which results in a conditional
contribution path. Subjects are randomly assigned roles of first- and second-movers
at the end of the experiment. For the type classification, only the contribution ta-
ble of a subject is considered. The classification of Fischbacher, achter, and Fehr
(2001) results in four types: a conditional cooperator whose contributions increase
with other players’ contributions, a selfish type who never cooperates, a triangle
cooperator with hump-shaped contributions, and the remaining subjects who do not
fit either one of the classifications.
Recently, there have been two proposals to refine the classification based on
Fischbacher, achter, and Fehr (2001): (i) the method of Th¨oni and Volk (2018),
which is based on the Pearson correlation coefficient and (ii) the method of Fallucchi,
Luccasen, and Turocy (2018), which is based on hierarchical clustering. We will
describe the behavioral types resulting from both refinements in Section 3.2. They
have in common that they entail a behavioral type whose description comes close to
the altruist in SPD: the unconditional cooperator (UC) in Th¨oni and Volk (2018)
and the unconditional high type (UHC) in Fallucchi, Luccasen, and Turocy (2018).
3

Citations
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Dissertation
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Abstract: There is a large body of empirical evidence that people do not always behave according to game theoretic predictions in many economic or social environments. Possible deviations from standard-economic behavior can occur when individuals have either (i) non-standard beliefs, which are systematically biased, (ii) non-standard preferences, such as preferences for fairness, or (iii) when they engage in imperfect utility maximization, for example, because of limited attention and only consider salient alternatives in their choice sets (Rabin, 2002). This thesis addresses issues related to such forms of boundedly rational behavior and non-standard utility maximization.

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Cites background from "Conditional cooperation: Type stabi..."

  • ...4The fourth chapter is based on Eichenseer and Moser (2019a)....

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  • ...The fourth chapter (Section 5) thematically ties in with the third chapter.4 While, I show in the third chapter that cooperation types have a high predictive 3This chapter is based on Eichenseer and Moser (2019b)....

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References
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Abstract: This article discusses the economic implications of reciprocity. A long-standing tradition in economics views human beings as exclusively self-interested. In most economic accounts of individual behavior and aggregate social phenomena, the vast forces of greed are put at the center of the explanation. However, many people deviate from purely self-interested behavior in a reciprocal manner. Reciprocity means that in response to friendly actions, people are frequently much nicer and much more cooperative than predicted by the self-interest model; conversely, in response to hostile actions they are frequently much more nasty and even brutal. There is considerable evidence that a substantial fraction of people behave according to this dictum: People repay gifts and take revenge even in interactions with complete strangers and even if it is costly for them and yields neither present nor future material rewards. This notion of reciprocity is thus very different from kind or hostile responses in repeated interactions that are solely motivated by future material gains.

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Abstract: We study the importance of conditional cooperation in a one-shot public goods game by using a variant of the strategy-method. We find that a third of the subjects can be classified as free riders, whereas 50 percent are conditional cooperators.

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TL;DR: Experimental measures of conditional cooperation and survey measures on costly monitoring among 49 forest user groups in Ethiopia with measures of natural forest commons outcomes show that groups vary in conditional cooperation, groups with larger conditional cooperator share are more successful in forest commons management, and costly monitoring is a key instrument with which conditional cooperators enforce cooperation.
Abstract: Recent evidence suggests that prosocial behaviors like conditional cooperation and costly norm enforcement can stabilize large-scale cooperation for commons management. However, field evidence on the extent to which variation in these behaviors among actual commons users accounts for natural commons outcomes is altogether missing. Here, we combine experimental measures of conditional cooperation and survey measures on costly monitoring among 49 forest user groups in Ethiopia with measures of natural forest commons outcomes to show that (i) groups vary in conditional cooperator share, (ii) groups with larger conditional cooperator share are more successful in forest commons management, and (iii) costly monitoring is a key instrument with which conditional cooperators enforce cooperation. Our findings are consistent with models of gene-culture coevolution on human cooperation and provide external validity to laboratory experiments on social dilemmas.

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