Santa Fe Institute

The friend of my enemy is my enemy

July 19, 2010 12:41 p.m.

A new study analyzing interactions between players in a virtual universe game has for the first time provided large-scale evidence to prove an 80-year-old psychological theory known as Structural Balance Theory.

Published July 19, 2010, in PNAS, the study shows that individuals tend to avoid stress-causing relationships when they develop a society, resulting in more stable social networks. It was carried out by Renaud Lambiotte of Imperial College London, Michael Szell at the Medical University of Vienna, and Stefan Thurner, an external professor at the Santa Fe Institute and head of the Complex Systems Research Group at the Medical University of Vienna.

The study analyzes relationships between 300,000 players in an online game called Pardus ( In this open-ended game, players act as spacecraft exploring a virtual universe, where they can make friends and enemies, and communicate, trade and fight with one another.

Scientists currently study data from people’s electronic interactions, such as emails, mobile phones, and online retail behaviour, to improve their understanding of human societies. Online games such as Pardus produce vast amounts of data that scientists can also use to study interactions between players, applying their findings to understanding the way that people interact in society.

Structural Balance Theory suggests that some networks of relationships are more stable than others in a society. Specifically, the theory deals with positive and negative links between three individuals, where ‘the friend of my enemy is my enemy’ is more stable (and therefore more common) than ‘the friend of my friend is my enemy’.

Information about interactions between players in Pardus is more detailed than that from other electronic sources because it includes data on the types of relationship and whether the interactions are positive or negative. This has enabled the authors of the study to show that positive relationships form stable networks in society.

As part of the study, mathematicians looked at six types of interaction between players in an online game: friendship, communication, trade, hostility, aggression, and punishment. Each one defines a network on its own; all six together combine to form one large network. A unique aspect of the data is that some of the links have a positive connotation (friendship, communication and trade), while others correspond to negative interactions (hostility, aggression and punishment).

The authors found that in positive relationships, players are more likely to reciprocate actions and sentiments than in negative ones. They also revealed strong interactions between different types of links, with some networks overlapping extensively, as players are likely to engage in similar interactions, and others tending to exclude each other. For example, friendship and communication networks overlap: as we would expect, friends tend to talk to each other. However, trade and hostility did not overlap at all, showing that enemies tend not to trade with one another.

The researchers are currently developing their mathematical tools for large, complex networks in order to study patterns of communication between millions of people from mobile phone data and also to examine biological problems such as the way different regions of the brain communicate with each other.

The work was funded by the Engineering and Physical Sciences Research Council ( and the Austrian Science Fund Fonds zur Förderung der wissenschaftlichen Forschung P 19132, and was conducted within the framework of EU COST Action MP0801 Physics of Competition and Conflicts.

The paper, “Trade, conflict, and sentiments: Multirelational organization of large-scale social networks,” appeared in PNAS on July 19, 2010.

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