Cooperation – All Just a Game?

An article from carl 03|2025

by Karin Hollricher

We all make decisions in our daily interactions with other people. But we aren't necessarily always aware why we decide for or against cooperation in individual cases. Can game theory explain the criteria according to which we act?

A joint undertaking by people is highly dependent on their willingness to collaborate. Selfless behaviour cannot be taken for granted, because each individual has selfish interests that do not necessarily support cooperative behaviour. Whether we’re talking about clearing snow for your neighbour, completing a contract or getting involved in environmental protection – people must make decisions day in day out. A mathematical theory – game theory – is used to determine the criteria according to which people make decisions and which mechanisms are truly effective here. The participants – or the players – are left to make decisions within defined rules.

Intuitively, we understand that we help people who reciprocate. In the language of game theory, this mechanism is called direct reciprocity. Originally, idealised prerequisites were assumed, such as that the participants have the same physical and economical resources, such as power, aids or financial means, and that the players are therefore interchangeable. But what happens if – like in real life – resources are unevenly distributed? “The influence of inequality on willingness to cooperate is a really hot topic in research,” said mathematician Christian Hilbe. He studied this issue during his time in the “Computer-based verification – game theory” working group run by Krishnendu Chatterjee at the Institute of Science and Technology Austria (ISTA) in Klosterneuburg. The researchers there modelled how a group responds when not all members of a group can contribute an equal number of resources to solve a task, but all can draw the same benefit [1]. What constitutes a resource is dependent on the example. Resources could be aids, like a tractor, but also money, expertise or the available time budget. The results of the simulations were interesting: a long-term, stable collaboration benefits from an equal distribution of resources, so that each member can make the same contribution. But if you want to complete a community effort efficiently, it is advantageous if those who have more resources are willing to get more involved.

The working group investigated what happens when the participants interact repeatedly under changing conditions, having to make new decisions and being able to change costs and benefits subsequently, depending on previous decisions. Games with this kind of feedback mechanism are called stochastic games.

They found that the players take higher costs into account and strengthen the cooperation when they understand that this can prevent an imminent deterioration of the situation in future – such as for protection of the environment and climate [2]. 

To make rational decisions, the participants need information. Earlier models assumed that the players were exactly aware of the external conditions, which were important for the game. Well-informed people or groups are able to successfully adapt their strategies based on their knowledge. “But as soon as there is scientific uncertainty, such as regarding the state of the ecological environment, the cooperation falls apart,” said Hilbe, who now manages his own research group at the Max Planck Institute for Evolutionary Biology in Plön. Surprisingly, uncertainty can also encourage collaboration – but this is very rare [3]. Hilbe: “When people don’t know the exact environment in which they are located, they do whatever is good for them on average. This can sometimes be better than if they do precisely what is best for themselves in every possible situation.”

Decisions are not only influenced by information and external conditions, but also by social norms. One such norm is, for example, that people tend only to help others if they have a good reputation. This norm leads to stable collaboration. How do such social norms come about and spread? And under which circumstances are they given up in favour of other norms? Hilbe: “There are thousands of social norms. Usually game theory models only take a few, very stable forms into account, because otherwise things get too complicated.” He and his colleague Yohsuke Murase from the RIKEN Centre for Computer Sciences in Kobe (Japan) were not deterred by this. They chose about 2000 norms and used a supercomputer to analyse the conditions under which they develop and change [4]. In contrast to previous assumptions, this revealed that cooperative norms, such as helping people with a good reputation, are difficult to maintain if the population is made up of individuals with different views. Differences of opinion with regard to the acceptance of a strategy result in division of the community.

Cooperations are more stable if smaller communities form within the population. Some social norms find it acceptable, for example, for help to be provided even if the other person’s reputation is not very good. The stern judging norm, in contrast, is a strict social rule that spreads quickly and strongly condemns such behaviour. Hilbe: “If stern judging is an accepted norm, groups soon form within which there is widespread cooperation, but which battle against each other. An indicator of this development is that there is no longer any neutrality.” This behaviour can definitely be observed in current world affairs.

[1] V. Hübner et al., 2024, PNAS 121, doi.org/10.1073/pnas.2315558121
[2] C. Hilbe et al., 2018, Nature 559, 246-249
[3] M. Kleshnina et al., 2023, Nature Comm. 14, 4153
[4] Y. Murase und C. Hilbe, 2024, PNAS 121, doi.org/10.1073/pnas.240688512

Image credits: freepik