One of the great unanswered question in biology is why organisms have evolved to cooperate. The long-term benefits of cooperation are clear—look at the extraordinary structures that termites build, for example, or the complex society humans have created.

But evolution is a random process based on the short-term advantages that emerge in each generation. Of course, individuals can cooperate or act selfishly, and this allows them to accrue benefits or suffer costs, depending on the circumstances. But how this behavior can spread and lead to the long-term emergence of cooperation as the dominant behavior is a conundrum that has stumped evolutionary biologists for decades.

Today, that could change thanks to the work of Christoph Adami and Arend Hintze at Michigan State University in East Lansing. They have created a simple mathematical model using well understood physical principles to show how cooperation emerges during evolution.

Their model suggests that the balance between cooperation and selfish behavior, called defection, can undergo rapid phase transitions, in which individuals match their behavior to their neighbors. What’s more, a crucial factor turns out to be the process of punishment. “Punishment acts like a magnetic field that leads to an 'alignment' between players, thus encouraging cooperation,” say Adami and Hintze.

This new approach has the potential to change the way evolutionary biologists, economists, and computer scientists think about cooperation and the role that punishment plays in encouraging it.

First some background. A wide range of phenomena depend on the large-scale behavior of many individual actors. For example: the economy, the spread of disease, evolution, Brownian motion, magnetization, to name just a few.

In some cases, the actors are relatively simple. In magnetization, for example, the actors are individual atoms with a spin that can be up or down and that interact with their neighbors.

At first glance, the way huge numbers of atoms interact in a magnetic material seems complex beyond imagination. But there is a relatively simple mathematical model called an Ising spin model that intuitively explains how magnetic domains form.

In this model, atoms can have a spin up or down and influence their neighbors. In the simplest case, atoms in a lattice start off with spins in random directions. But they can flip their spins in a way that depends on the spins of their neighbors. An external magnetic field can also cause the spins to align provided the temperature is below some critical level.

Using this model, physicists can explore the circumstances in which domains emerge where all the atoms share the same spin. They can also explore how this depends on environmental factors such as temperature and an external magnetic field.

The question that Adami and Hintze investigate is whether an Ising spin model can throw some light on the way cooperation evolves.

To find out, they created an Ising spin model in which each “atom” interacts with its neighbors by either cooperating or defecting in a game of prisoner’s dilemma. In this game between two atoms, each player can either cooperate or defect and then receive a payout that depends on the behavior of the other player.

The players receive a reward if they both cooperate but nothing if they both defect. However, the dilemma occurs because the highest payout is given to a player who defects whilst the opponent cooperates, who then gets nothing.

At the end of the game, each atom can change its strategy to that of its neighbor or not, depending on how successful the neighbor has been.

The distribution of strategies is random to start with. But over time, this process should lead to the spread of successful strategies in an analogous process to the formation and spread of magnetic domains.

Adami and Hintze’s work is in exploring the thermodynamics of this process, the conditions in which cooperation spreads.

Their results make for fascinating reading. It turns out that the strategies of cooperation and defection are in a delicate balance, but that in some circumstances, a phase transition occurs in which cooperation spreads through the population like wildfire. Indeed, Adami and Hintze say there is a formal mathematical analogy with magnetism in this respect.

They also generalize the system to include more “atoms” playing the well-known public goods game. In this game, each player has a pot of money and has to decide how much to put into the public purse, where it will be multiplied by some number greater than 1. This is then redistributed to all the players equally.

Obviously, players have the most to gain if they all put all their money in the public purse. But a single player can gain more by putting nothing in and reaping the reward.

Adami and Hintze also introduce punishment. So atoms that do not contribute can be made to suffer a cost.

In this case, punishment has a profound effect. “Punishment acts like a magnetic field that encourages alignment of spins,” say the researchers.

That’s an interesting result. It implies that behavior can be manipulated on a large scale by the introduction of certain costs. It also implies that the result can be modeled using relatively simple physics.

Interestingly, physicists have developed a wide range of techniques to study these kinds of spin systems in considerable detail. The biggest significance of Adami and Hintze’s work is that this mathematical machinery can now be brought to bear on the problem of cooperation.

That should bring more insight in the not-too-distant future. And it could have enormous implications for the way sociologists, economists, and policy makers think about the nature of society and way it can be manipulated in the future.

Ref: arxiv.org/abs/1706.03058: Thermodynamics of Evolutionary Games