Collaborative hierarchy maintains cooperation in asymmetric games

www.nature.com/scientificreports OPEN Collaborative hierarchy maintains cooperation in asymmetric games Alberto Antonioni1,2,3, María Pereda2,4,5, Katherine A. Cronin6, Marco Tomassini7 & Angel Sánchez 2,3,4,8 Received: 15 November 2017 Accepted: 12 March 2018 Published: xx xx xxxx The interplay of social structure and cooperative behavior is under much scrutiny lately as behavior in social contexts becomes increasingly relevant for everyday life. Earlier experimental work showed that the existence of a social hierarchy, earned through competition, was detrimental for the evolution of cooperative behaviors. Here, we study the case in which individuals are ranked in a hierarchical structure based on their performance in a collective effort by having them play a Public Goods Game. In the first treatment, participants are ranked according to group earnings while, in the second treatment, their rankings are based on individual earnings. Subsequently, participants play asymmetric Prisoner’s Dilemma games where higher-ranked players gain more than lower ones. Our experiments show that there are no detrimental effects of the hierarchy formed based on group performance, yet when ranking is assigned individually we observe a decrease in cooperation. Our results show that different levels of cooperation arise from the fact that subjects are interpreting rankings as a reputation which carries information about which subjects were cooperators in the previous phase. Our results demonstrate that noting the manner in which a hierarchy is established is essential for understanding its effects on cooperation. While cooperation is common in many species1–3, humans show this trait to a dramatically larger extent. This is evident in our unparalleled capability to cooperate with strangers in one-shot interactions and on a very large scale4–6. The emerging phenomenon of cooperation can involve working together with others in a mutually beneficial activity (i.e., a form of mutualism7), or incurring a costly action that helps others, thus reducing one’s own chances for survival under natural selection (i.e., altruism8). Both types of cooperation are ubiquitous in our daily lives, and constitute the pillar on which our society is built and functions9. However, for all its importance, the interplay between social structure and cooperative behavior in humans has received little attention10. In this context, it has been shown that active partner choice, i.e., the possibility to choose interaction partners at will or through assortment11, does lead to the establishment of cooperation12,13. However, past experimental work has rarely allowed social interaction, employing paradigms where all individuals were equal and anonymous, and choices motivated only by informational cues (i.e., reputation14–16,). In most social interactions, some degree of asymmetry or inequality between positions in the network is a key factor. Particularly among primates, hierarchy or ranking is a determinant factor in the decision to work with another individual1,10. Even the mere presence of another, differently ranked subject has been shown to dramatically affect individuals’ performance17. Once not all individuals have the same strategic options and/or the consequences of their actions differ, those in a superior position can reap more benefits from cooperative actions at the expense of their partners, which in turn may lead the latter to stop cooperating. It has been shown recently18 that this is also the case in experiments with humans designed similarly to setups employed with primates19,20: Lower ranked subjects contribute less to a common goal when they benefit less than their partners. Interestingly, this appears to be due to the fact that when higher ranked subjects can coerce their counterparts into cooperating, they very often do so21 by resorting to so-called zero-determinant strategies22,23. It thus seems that the existence 1 Department of Economics, University College London, London, UK. 2Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911, Leganés, Madrid, Spain. 3Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018, Zaragoza, Spain. 4 Unidad Mixta de Comportamiento y Complejidad Social, UC3M-UV-UZ (UMICCS), Leganés, Spain. 5RWTH Aachen University, Chair for Computational Social Sciences and Humanities, Aachen, Germany. 6Lester E. Fisher Center for the Study and Conservation of Apes, Lincoln Park Zoo, Chicago, IL, USA. 7Information Systems Department, Faculty of Business and Economics, University of Lausanne, CH-1015, Lausanne, Switzerland. 8UC3M-BS Institute for Financial Big Data (IFiBiD), Universidad Carlos III de Madrid, 28903, Getafe, Madrid, Spain. Correspondence and requests for materials should be addressed to A.A. (email: ) SCIEnTIFIC RePorTS | (2018) 8:5375 | DOI:10.1038/s41598-018-23681-z 1 www.nature.com/scientificreports/ Figure 1. Sketch of the hierarchy assignment procedures. The 24 participants are ranked with respect to their cumulated payoff at the end of Phase I (numbers from 1 to 24) while the six groups are ranked according to the sum of individual payoffs of their group components. The four hierarchy profiles are divided into two class types: high (A,B) and low (C,D). of a social structure, in the form of a ranking or a hierarchy, can have detrimental effects in the stability of cooperation among humans. In this study we want to probe further into the interplay of social structure and cooperation by considering a different type of hierarchy. This is by no means an academic question in so far as hierarchies differ among primate species in their steepness and their linearity24, and organizations in our society come in very different flavors and structures25. Therefore, here we set out to study how cooperation is affected when hierarchies are not linear but instead there is more than one individual at each ranking level. Additionally, we contribute to the knowledge of cooperation on hierarchical structure by considering the case in which one’s ranking arises through competition with all others as in18, or through some amount of cooperation. We study these issues by means of a novel experimental design, which, as we will see below, allow us to shed light on hitherto unexplored facets of cooperative behavior. As shown in previous experimental works8,26–29, when pairwise interactions are repeated for a reasonably large number of rounds the mutual cooperation outcome is easier to achieve. Here, we employ a setting for testing the impact of hierarchy formation in short, but not one-shot, interactions, avoiding the direct reciprocity mechanism present for longer time encounters. Experimental Setup The experimental setup we introduce in this work consists of three treatments, namely Selfish (or Competitive) Hierarchy (SH), Collaborative Hierarchy (CH) and Random Hierarchy (...truncated)