Direct reciprocity facilitates cooperation in repeated social interactions. Traditional models suggest that individuals learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. However, most existing models make rather strong assumptions about how individuals decide to keep or change their strategies.

They assume individuals make these decisions based on a strategy’s average performance. This in turn suggests that individuals would remember their exact payoffs against everyone else.

In a recent study, researchers from the Max Planck Institute for Evolutionary Biology, the School of Data Science and Society, and the Department of Mathematics at the University of North Carolina at Chapel Hill examine the effects of realistic memory constraints. They find that cooperation can evolve even with minimal memory capacities. The research is published in the journal Proceedings of the Royal Society B: Biological Sciences.

Direct reciprocity is based on repeated interactions between two individuals. This concept, often described as “you scratch my back, I’ll scratch yours,” has proven to be a pivotal mechanism in maintaining cooperation within groups or societies.

While models of direct reciprocity have deepened our understanding of cooperation, they frequently make strong assumptions about individuals’ memory and decision-making processes. For example, when strategies are updated through social learning, it is commonly assumed that individuals compare their average payoffs.

This would require them to compute (or remember) their payoffs against everyone else in the population. To understand how more realistic constraints influence direct reciprocity, the current study considers the evolution of conditional behaviors when individuals learn based on more recent experiences.

Two extreme scenarios

This study first compares the classical modeling approach with another extreme approach. In the classical approach, individuals update their strategies based on their expected payoffs, considering every single interaction with each member of the population (perfect memory). Conversely, the opposite extreme is considering only the very last interaction (limited memory).

Comparing these two scenarios shows that individuals with limited payoff memory tend to adopt less generous strategies. They are less forgiving when someone defects against them. Yet, moderate levels of cooperation can still evolve.

Intermediate cases

The study also considers intermediate cases, where individuals consider their last two or three or four recent experiences. The results show that cooperation rates quickly approach the levels observed under perfect payoff memory.

Overall, this study contributes to a wider literature that explores which kinds of cognitive capacities are required for reciprocal altruism to be feasible. While more memory is always favorable, reciprocal cooperation can already be sustained if individuals have a record of two or three past outcomes.

This work’s results have been derived entirely within a theoretical model. The authors feel that such studies are crucial for making model-informed deductions about reciprocity in natural systems.

How do particles move in turbulent fluids? The answer to this question can be found in a new model presented in a thesis from the University of Gothenburg. The model could help speed up the development of new drugs.

When you stir a glass of water, it is easy to think that any particles in the water will end up in chaos and move completely randomly. But this is not always the case. For example, the so-called active micro-swimmers can move through flow on their own.

Navid Mousavi, a Ph.D. student at the University of Gothenburg, has created a model including various hydrodynamic factors to study how these particles handle and even utilize turbulence.

Micro-swimmers can be biological, such as plankton, or engineered particles such as nanomotors. Plankton contribute to global ecosystems by producing oxygen and they form the basis of the ocean food web.

Free-riding in the current

Navid Mousavi has created new methods for modeling and studying the navigation of micro-swimmers by combining active matter physics with machine learning principles. The thesis finds optimal behaviors for plankton to survive in their turbulent habitat.

“In the model, plankton use local information for navigation, reflecting the real-world conditions that these small swimmers encounter. Unlike previous models where navigation was based on global information,” says Navid Mousavi.

The research also showed that micro-swimmers can utilize the flow to move faster than they can on their own, which is an important insight for both biological and artificial applications.

Another exciting result of the study is the discovery of optimal behavior to avoid high turbulent strain. Surprisingly, it is observed that micro-swimmers tend to swim against the current to keep their position in low-strain regions.

“This behavior seems to be crucial for survival and allows plankton to avoid predators and stay in nutrient-rich zones,” says Navid Mousavi.

Important knowledge for medicine development

All the strategies found were shown to work effectively in several different scenarios, meaning they can be applied to real-life situations.

The results of the study provide important knowledge that has several applications. An example is in medicine, where it could help develop smart micro-swimmers that can deliver drugs directly to specific areas of the body, making treatments more effective. Environmentally, these tiny swimmers could help clean up microplastics from our oceans and contribute to a healthier planet.

“In the future, we will need to validate the model in experiments, both with natural plankton and artificial micro-swimmers,” says Navid Mousavi.

The researchers also plan to investigate more complex models that deal with energy efficiency and the collective behavior of multiple swimmers.