Game Theory 7: Cooperative Games


Game theory is the study of interdependent interactions between adaptive agents, and when we look at these interactions between agents in the world around us we see elements of both competition and cooperation.

We see the organelles within a biological cell work together to enable its overall functioning. We see organisms within ecosystems forming symbiotic cooperative relations. We see people form families, tribes, cities, and nations all of which involve high levels of cooperation.

Game theory should then be a tool that helps us to understand what actions an agent should take within non-cooperative situations and what outcomes are most likely in such games.

But it should also be a tool that helps us understand how cooperation works. The first thing for us to note is that the dynamics of cooperation are very different from those that we have been studying in games of noncooperation. Cooperative dynamics rewrite the rules of the games people play.

In non-cooperative games like the prisoner’s dilemma, we noted how individual rationality, in fact, led to collective irrationality. We called this a dilemma and lamented the fact that within the non-cooperative framework of self-interested individuals there was nothing we could do about it. However, we as humans do not just look out for our own interests but also those of others and in so doing we have evolved highly sophisticated means for cooperation in the process.

When we add this new element to the game, that of cooperation, we now have the possibility for the agents to solve this dilemma. The question then turns to how and when do coalitions for cooperation form, where we can achieve both stable and optimal outcomes for the individual and the whole organization.

With non-cooperative games, we are solely focused on the payoffs to the individuals and searching for stable situations. Cooperative game theory, however, adds an extra dimension to this in that we now have to think about the payoff to the whole organization. In such a case we can not simply look a the actions of the individuals and their payoffs but we have to also look at the positive or negative externalities that these actions may have on the whole system.


Cooperation is a process by which the components of a system work together to achieve the global properties. In other words, individual components that appear independent work together to create a complex whole, greater-than-the-sum-of-its-parts system.

Virtually all of human civilization is a product of our capacity to work cooperatively. Indeed the complex systems that surround us, like our global economy and technologies like a jumbo jet are a testament to our extraordinary capacity for cooperation.

In most animal groups and even our closest relatives in the primate group, competition is the norm, and cooperation occurs largely only among kin, who have common genes and so have a biological incentive to do so, or else among a few individuals who cooperate reciprocally. But humans cooperate with each other in very large groups in a multiplicity of ways.

People risk their lives in war for their countrymen and we make sure that our less fortunate compatriots have enough food and medical care to survive. On a daily basis, we obey all kinds of prosocial norms. And when we do breach some prosocial norm, like not doing our part in a collective enterprise, we feel guilty or ashamed, in general, we are highly sensitive to cooperative behavior.

Human evolved capacity for cooperation is a cultural one that distinguishes us from other creatures who we may share up to 98% of our genes in common with. A large-scale study has recently provided some foundation to this hypothesis.

Researchers compared two-year-old children to their nearest primate relative chimpanzees and orangutans. They were all given 16 different tasks grouped into two overall categories. One concerning an understanding of the physical world, the other an understanding of the social world. The physical tests were related to space, quantity, and causality, and the social tests concerned capacities for social imitation, communication, and intention reading. The experiment revealed that the children were not across the board more intelligent than the primate animals, but in fact only with respect to social cognition were they more advanced. At just two years of age, the children were already about twice as high on this indicator as the other two creatures. This social capacity enables us to take advantage of the skills and knowledge of others within a social group through cooperation.

The researchers noted that apes did have social cognitive skills, but they were mainly using their social understanding of others within contexts of competition. From this, the researchers proposed that on top of great apes skills for social cognition humans had evolved additional social cognitive capabilities for dynamics of cooperation, which involve greater complexity, but which can ultimately be seen as the foundations to advanced forms of civilization.

Thus they came to understand others as not just intentional goal seeking agents, but also as potential cooperative agents with whom they could work together to produce outcomes that neither could produce alone. This cognitive capacity along with communications enabled us to create the ever more complex social and cultural institutions for cooperation, that today form the foundation of our advanced systems of socio-economic coordination.

The researchers claimed that this distinction between apes and humans can be identified even in the earliest human economies. Noting how apes are individual foragers, where they will travel in small groups until they find a food source like a fig tree and then run up and grab the food separately without collaboratively producing it or sharing it. Humans, however, are collaborative foragers meaning that most traditional forager groups derive most of their daily nutrition from collaborative activities in different forms, such as hunting.

This is not to say that advanced forms of cooperation do not happen within other creatures. We just have to look at ant or bee colonies to see sophisticated coordination. However, these creatures have nowhere near the kind of individual cognitive capacity that apes and humans do, and thus we do not get the same kind of complex dynamic between the individual and the group that is at the heart of human social systems and the study of cooperation.

Dynamics of cooperation require more cognitive capabilities on the behalf of the individual because they are greatly more complex in nature than noncooperative situations.

Whereas non-cooperative dynamics are governed solely by the self-interest of the individual’s, cooperation involves a new level of organization, that of the group, and a complex dynamic between the individual and the overall group.

This central dynamic within cooperation is captured in the idea of the social dilemma. Social dilemmas are characterized by two properties: The social payoff to each individual for defecting behavior is higher than the payoff for cooperative behavior, regardless of what the other society members do, yet all individuals in the society receive a lower payoff if all defect than if all cooperate. It is a situation where individual rational behavior leads to a situation where everyone is worse off.

Social dilemmas are of interest to many because they reveal the core tension between the individual and the group, that is engendered in situations of cooperation. At their core, social dilemmas are situations in which self-interest is at odds with collective interests and they can be found in many situations of interdependence; from resource management to relationship development, to international politics, public goods provision and business management. In the next section, we will zoom in to look more closely at the workings of this social dilemma.