Abstract
This article studies human connections by examining the helping game—a hybrid between the classic two-player and multi-player prisoner’s dilemma. In the helping game, players are presented with a pool of heterogeneous players and have to decide whom to help, if any. Helping others is associated with a cost unique to each potential partner, and receiving help is associated with a fixed benefit. An economic experiment was conducted with 100 students to analyse under which circumstances partnerships (defined as both helping each other) develop in the game. The findings indicate that partnerships form in the game, although mainly when providing help is relatively cheap for both parties. Therefore, most partnerships are between lower helping-cost players, while higher helping-cost players struggle to form partnerships. In addition, establishing partnerships is easier when players meet potential partners consecutively rather than simultaneously, as long as helping others is not too costly. Moreover, less risk-tolerant subjects provide more help to reduce the risk of not forming partnerships, yet establish fewer partnerships, as less risk-tolerant players avoid helping others when it is costly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author upon request.
Notes
In this paper the cost parameter has been slightly modified from Rivas (2009) to fit a more general case. In Rivas, the cost parameter consists of two components, the player’s helping need ci and a fixed helping cost p. Hence, the cost of providing help becomes ci p. In the current study, it is assumed that helping a player is only associated with a player specific cost ci. This generalisation does not change the overall cost benefit structure of the model, nor does it change the predicted outcomes.
A sensitivity power analysis of the sample size was conducted in G*Power (Faul et al. 2007), and the results are presented in Tables 16 and 17, in the appendices. In general, following Cohen (1988, 1992), the study has enough power to detect medium to large effect sizes. Moreover, comparing the effect sizes for which the study has ex ante sufficient power with the actual observed effect sizes shows that most results in this paper are supported by sufficient statistical power. The few exceptions are discussed in detail throughout the text.
Most subjects (72%) started with the saver lottery B and then switched to the riskier lottery A as the likelihood of the favourable outcome in lottery A increased. However, some subjects (28%) switched back to the safe lottery B at some point. This observation is line with other studies which have found similar rates of switching back (see, for example, Holt and Laury (2002); Anderson and Mellor (2008)).
References
Ahn TK, Isaac RM, Salmon TC (2008) Endogenous group formation. J Public Econ Theory 10(2):171–194. https://doi.org/10.1111/j.1467-9779.2008.00357.x
Aimone JA, Iannaccone LR, Makowsky M, Rubin J (2013) Endogenous group formation via unproductive costs. REStud 80(4):1215–1236. https://doi.org/10.1093/restud/rdt017
Anderson LR, Mellor JM (2008) Predicting health behaviors with an experimental measure of risk preference. J Health Econ 27(5):1260–1274. https://doi.org/10.1016/j.jhealeco.2008.05.011
Ashlock D, Smucker MD, Stanley EA, Tesfatsion L (1996) Preferential partner selection in an evolutionary study of prisoner’s dilemma. BioSystems 37(1–2):99–125. https://doi.org/10.1016/0303-2647(95)01548-5
Au WT, Lu S, Leung H, Yam P, Fung JM (2012) Risk and prisoner’s dilemma: a reinterpretation of Coombs’ re-parameterization. J Behav Decis Mak 25(5):476–490. https://doi.org/10.1002/bdm.743
Bonacich P, Shure GH, Kahan JP, Meeker RJ (1976) Cooperation and group size in the n-person prisoners’ dilemma. J Conflict Resolut 20(4):687–706. https://doi.org/10.1177/002200277602000406
Bone JE, Wallace B, Bshary R, Raihani NJ (2015) The effect of power asymmetries on cooperation and punishment in a prisoner’s dilemma game. PloS One 10(1):e0117183. https://doi.org/10.1371/journal.pone.0117183
Brekke KA, Hauge KE, Lind JT, Nyborg K (2011) Playing with the good guys. A public good game with endogenous group formation. J Public Econ 95(9–10):1111–1118. https://doi.org/10.1016/j.jpubeco.2011.05.003
Cohen J (1988) Statistical power analysis for the social sciences, 2nd edn. Lawrence Erlbaum Associates, Hillsdale, New Jersey
Cohen J (1992) A power primer. Psychol Bull 112(1):155–159. https://doi.org/10.1037/0033-2909.112.1.155
Dal Bó P (2005) Cooperation under the shadow of the future: experimental evidence from infinitely repeated games. Am Econ Rev 95(5):1591–1604. https://doi.org/10.1257/000282805775014434
Dal Bó P, Fréchette GR (2011) The evolution of cooperation in infinitely repeated games: experimental evidence. Am Econ Rev 101(1):411–429. https://doi.org/10.1257/aer.101.1.411
Dal Bó P, Fréchette GR (2018) On the determinants of cooperation in infinitely repeated games: a survey. J Econ Literature 56(1):60–114. https://doi.org/10.1257/jel.20160980
Dal Bó P, Fréchette GR (2019) Strategy choice in the infinitely repeated prisoner’s dilemma. Am Econ Rev 109(11):3929–3952. https://doi.org/10.1257/aer.20181480
Dreber A, Rand DG, Fudenberg D, Nowak MA (2008) Winners don’t punish. Nature 452(7185):348–351. https://doi.org/10.1038/nature06723
Duffy J, Ochs J (2009) Cooperative behavior and the frequency of social interaction. Games Econom Behav 66(2):785–812. https://doi.org/10.1016/j.geb.2008.07.003
Dunbar RI (2018) The anatomy of friendship. Trends Cogn Sci 22(1):32–51. https://doi.org/10.1016/j.tics.2017.10.004
Faul F, Erdfelder E, Lang A-G, Buchner A (2007) G*Power 3: a flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav Res Methods 39(1):175–191. https://doi.org/10.3758/BF03193146
Fehr E, Gächter S (2002) Altruistic punishment in humans. Nature 415(6868):137–140. https://doi.org/10.1038/415137a
Fernández-Domingos E, Loureiro M, Alvarez-López T, Burguillo JC, Covelo J, Peleteiro A, Byrski A (2017) Emerging cooperation in n-person iterated prisoner’s dilemma over dynamic complex networks. Comput Inf 36(3):493–516. https://doi.org/10.4149/cai_2017_3_493
Fischbacher U (2007) z-Tree: Zurich toolbox for ready-made economic experiments. Exp Econ 10(2):171–178. https://doi.org/10.1007/s10683-006-9159-4
Fischbacher U, Gächter S (2010) Social preferences, beliefs, and the dynamics of free riding in public goods experiments. Am Econ Rev 100(1):541–556. https://doi.org/10.1257/aer.100.1.541
Fischbacher U, Gächter S, Fehr E (2001) Are people conditionally cooperative? Evidence from a public goods experiment. Econ Lett 71(3):397–404. https://doi.org/10.1016/S0165-1765(01)00394-9
Fréchette GR, Yuksel S (2017) Infinitely repeated games in the laboratory: four perspectives on discounting and random termination. Exp Econ 20(2):279–308. https://doi.org/10.1007/s10683-016-9494-z
Glöckner A, Hilbig BE (2012) Risk is relative: risk aversion yields cooperation rather than defection in cooperation-friendly environments. Psychon Bull Rev 19(3):546–553. https://doi.org/10.3758/s13423-012-0224-z
Gürerk Ö, Irlenbusch B, Rockenbach B (2006) The competitive advantage of sanctioning institutions. Science 312(5770):108–111. https://doi.org/10.1126/science.1123633
Haesevoets T, Bostyn DH, Reinders Folmer C, Roets A, Van Hiel A (2019) Decision making in the prisoner’s dilemma game: the effect of exit on cooperation and social welfare. J Behav Decis Mak 32(1):61–78. https://doi.org/10.1002/bdm.2096
Hauert C, Traulsen A, Brandt H, Nowak MA, Sigmund K (2007) Via freedom to coercion: the emergence of costly punishment. Science 316(5833):1905–1907. https://doi.org/10.1126/science.1141588
Hauk E (2003) Multiple prisoner’s dilemma games with (out) an outside option: an experimental study. Theor Decis 54(3):207–229. https://doi.org/10.1023/A:1027385819400
Hauk E, Nagel R (2001) Choice of partners in multiple two-person prisoner’s dilemma games: an experimental study. J Conflict Resolut 45(6):770–793. https://doi.org/10.1177/0022002701045006004
Hennig-Schmidt H, Leopold-Wildburger U (2014) The shadow of the past: how experience affects behavior in an iterated prisoner’s dilemma experiment. J Bus Econ 84(6):865–878. https://doi.org/10.1007/s11573-014-0707-7
Holt CA, Laury SK (2002) Risk aversion and incentive effects. Am Econ Rev 92(5):1644–1655. https://doi.org/10.1257/000282802762024700
Jackson MO, Rogers BW (2007) Meeting strangers and friends of friends: how random are social networks? Am Econ Rev 97(3):890–915. https://doi.org/10.1257/aer.97.3.890
Jackson MO, Wolinsky A (1996) A strategic model of social and economic networks. J Econ Theory 71(1):44–74. https://doi.org/10.1006/jeth.1996.0108
Johnson DD (2016) Anthropology: hand of the gods in human civilization. Nature 530(7590):285–287. https://doi.org/10.1038/nature16879
Mac Carron P, Kaski K, Dunbar R (2016) Calling Dunbar’s numbers. Soc Netw 47(1):151–155. https://doi.org/10.1016/j.socnet.2016.06.003
Mailath GJ, Samuelson L (2006) Repeated games and reputations: long-run relationships. Oxford University Press, Oxford
Murnighan JK, Roth AE (1983) Expecting continued play in prisoner’s dilemma games: a test of several models. J Conflict Resolut 27(2):279–300. https://doi.org/10.1177/0022002783027002004
Nerurkar P, Chandane M, Bhirud S (2019) Measurement of network-based and random meetings in social networks. Turk J Electr Eng Comput Sci 27(2):765–779. https://doi.org/10.3906/elk-1806-103
Normann HT, Wallace B (2012) The impact of the termination rule on cooperation in a prisoner’s dilemma experiment. Int J Game Theory 41(3):707–718. https://doi.org/10.1007/s00182-012-0341-y
Orbell JM, Schwartz-Shea P, Simmons RT (1984) Do cooperators exit more readily than defectors? Am Polit Sci Rev 78(1):147–162. https://doi.org/10.2307/1961254
Perc M, Jordan JJ, Rand DG, Wang Z, Boccaletti S, Szolnoki A (2017) Statistical physics of human cooperation. Phys Rep 687(1):1–51. https://doi.org/10.1016/j.physrep.2017.05.004
Rand DG, Nowak MA (2013) Human cooperation. Trends Cogn Sci 17(8):413–425. https://doi.org/10.1016/j.tics.2013.06.003
Rezaei G, Kirley M (2012) Dynamic social networks facilitate cooperation in the N-player prisoner’s dilemma. Physica A 391(23):6199–6211. https://doi.org/10.1016/j.physa.2012.06.071
Rivas J (2009) Friendship selection. Int J Game Theory 38(4):521–538. https://doi.org/10.1007/s00182-009-0168-3
Sabater-Grande G, Georgantzis N (2002) Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test. J Econ Behav Organ 48(1):37–50. https://doi.org/10.1016/S0167-2681(01)00223-2
Selten R, Mitzkewitz M, Uhlich GR (1997) Duopoly strategies programmed by experienced players. Econometr J Econometr Soc 65(3):517–555. https://doi.org/10.2307/2171752
Strømland E, Tjøtta S, Torsvik G (2018) Mutual choice of partner and communication in a repeated prisoner’s dilemma. J Behav Exp Econ 75:12–23. https://doi.org/10.1016/j.socec.2018.05.002
Szolnoki A, Perc M (2010) Reward and cooperation in the spatial public goods game. EPL (Europhys Lett) 92(3):38003. https://doi.org/10.1209/0295-5075/92/38003
Acknowledgements
I would like to sincerely thank the Faculty of Arts and Social Sciences at the University of Surrey for funding the data collection process. I would also like to thank all the participants for taking the time to participate in this study. Further I am grateful for the constructive feedback that I received from the anonymous reviewers and the associate editor of this journal.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendices
1.1 Appendix A: Additional tables and figures
See Tables 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. See Fig. 4.
Average cooperation rates over time by cost group and meeting process. The variable rounds exclude the first four rounds for the consecutive meeting treatment
1.2 Appendix B: Experimental instructions
Welcome and thank you for taking part in this decision-making experiment. The study will last up to 1 h. Please read the instructions very carefully. As a result of the decisions you make during the experiment, you will accumulate fictional money. At the end of the experiment the fictional money will be paid out in cash. In this experiment, you have been placed into a group with 9 other individuals. All participants have been randomly allocated to a computer terminal and assigned a unique player number which will stay fixed throughout the experiment. Please note that during the study, no form of communication (talking, texting etc.) will be allowed. If you have any questions, please raise your hand and the experiment leader will come to your place.
During the experiment the currency is units. At the end of the experiment 50 units will be equal to 1 Pound. In the experiment you have to decide if you want to help other players or not. Helping another player is associated with a cost which is different for each player. At the start of the experiment you will be given 100 units which you can use to help other players. If you decide to help someone you have to pay the associated cost which will be indicated in the experiment. When a player helps you you´ll receive 12 units. In each round you can only help a maximum of four players. After each round the experiment will end with a probability of 1/12 (8.3%) and otherwise continue on to the next round. There is no maximum number of rounds.
Comprehension Questions:
Please fill out the following examples to make sure that you have understood the experiment. If you have any questions please feel free to ask the experiment leader.
Example 1) You are helping a player with helping cost 1, he isn’t helping you in return what is your payoff? _________________.
Example 2) Your helping costs are 3 and you are helping a player who is helping you in return. What is his payoff? _________________.
Example 3) Your helping cost is 2 and you are helping a player with helping cost 6, he/she is helping you in return what are your and his/her payoffs at the end of the round?
You: ____________________.
His/Her: _________________.
1.3 Appendix C: Experimental design
See Figs.
Game screenshot decision. Players could not help themselves. If a player tried to help themselves an error message showed up on the screen
5 and
Game screenshot outcome
6. Table
18.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Al Lily, M. Establishing human connections: experimental evidence from the helping game. Int J Game Theory 52, 805–832 (2023). https://doi.org/10.1007/s00182-023-00841-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-023-00841-8