There are many formal models that try to simulate competitive and cooperative dynamics; Prisoner’s Dilemma (PD) is one such popular example, being often referenced in game theory, economics, and evolutionary biology. I wanted to explore the intersection of these ideas with morphogenesis: the obvious (but still poorly-understood) alignment of cells toward a goal in anatomical morphospace: a specific large-scale outcome which the collective will pursue despite a wide range of perturbations and barriers. Thus, Lakshwin Shreesha and I set out to see if game theory models of rational agents making decisions could be harnessed to explain and control morphogenesis.
We used simulations of iterated, spatialized PD – each agent on a 2D grid plays against its local neighbors, repeatedly. But, there’s one key thing missing from the standard formalism: in typical game theory models, there is a fixed set of players. That is, there is a set of agents and a payoff table for the various actions, but there is one level of agency and their actions cannot change this basic structure. Life is not like that; part of the magic of material we call “alive” is that it can bind together into larger-scale systems (expanding the cognitive light cone of parts and projecting it into new problem spaces, such as the move from the physiological space that cells navigate to anatomical morphospace) or fragment (dissociate and scale down the size of the Self – as in the dissociative identity disorder of multicellularity we call cancer). But this ability to scale the Self dynamically fundamentally changes how game theory modeling works.
Consider the slime mold Physarum: (video below made by my former post-doc Nirosha Murugan for this paper)
Let’s say it begins to elongate toward a food target. Modeling this decision is simple – “go get the food”. But then an experimenter comes along and cuts the leading 10% of it off from the rest (see here for some actual data on this, which was part of a home-school study unit I did with my kids). Now something very interesting happens. The separated little blob has a decision to make: I can go get the food for myself, and not share it with the rest of the mass (huge energy density win for me!), or, I can move backwards and re-merge with the rest and then “we” will go get the food. Of course I’m not claiming the Physarum is symbolically or linguistically having those thoughts, this is just a way of framing the possible options and their adaptive payoffs as we study the evolutionary implications of different behavioral strategies. The key thing here is that if it were to re-merge, the selfish question of “grab the food and not share it” becomes meaningless – the system will be a syncitium and make decisions as a whole. Such calculus is only relevant while there is a separate agent that can be the subject of this payoff table. So, what is happening here is that the actions of an individual actually change how many individuals there will be – a very meta aspect, because the payoff table (and the number of entries in it) is actually plastic, and shifts dynamically during the simulation. Based on what you do, you may or may not exist in the future, so your relationship with Future You is radically altered. To my knowledge this has not been explored before (the closest thing I’ve been able to find, to such dynamic payoff tables, is hyperbolic discounting).
In order to enable such complex feedback between decisions and the number of agents able to make decisions, we modified PD: agents can now cooperate or defect, on each turn, but they can also Merge (with a neighbor) or Split. Now this more closely mimics the dynamic spectrum between multicellularity and cancer. All of the details and data are in this paper, summarizing the project implemented by Lakshwin Shreesha, Federico Pigozzi, and Adam Goldstein in my group. Here’s the Abstract:
Evolutionary developmental biology, biomedicine, neuroscience, and many aspects of the social sciences are impacted by insight into forces that facilitate the merging of active subunits into an emergent collective. The dynamics of interaction between agents are often studied in game theory, such as the popular Prisoner’s Dilemma (PD) paradigm, but the impact of these models on higher scales of organization, and their contributions to questions of how agents distinguish borders between themselves and the outside world, are not clear. Here we applied a spatialized, iterated PD model to understand the dynamics of the formation of large-scale tissues (colonies that act as one) out of single cell agents. In particular, we broke a standard assumption of PD: instead of a fixed number of players which can Cooperate or Defect on each round, we let the borders of individuality remain fluid, enabling agents to also Merge or Split. The consequences of enabling agents’ actions to change the number of agents in the world result in non-linear dynamics that are not known in advance: would higher-level (composite) individuals emerge? We characterized changes in collective formation as a function of memory size of the subunits. Our results show that when the number of agents is determined by the agents’ behavior, PD dynamics favor multicellularity, including the emergence of structured cell-groups, eventually leading to one single fully-merged tissue. These larger agents were found to have higher causal emergence than smaller ones. Moreover, we observed different spatial distributions of merged connectivity vs. of similar behavioral propensities, revealing that rich but distinct structures can coexist at the level of physical structure and the space of behavioral propensities. These dynamics raise a number of interesting and deep questions about decision-making in a self-modifying system that transitions from a metabolic to a morphological problem space, and how collective intelligences emerge, scale, and pattern.
Watch a talk here, that explains in detail what we did and what we found:
And, you can play with the simulations yourself, here:
If you find anything interesting there, let us know! I will just mention a few key findings from our paper:
- Over time, it appears this dynamic favors multicellularity – regions are formed, which get bigger. And that’s without any of the usual drivers that have been proposed to cause multicellularity (need to get bigger to avoid being eaten, etc.)
- Remarkably, larger higher-level agents have greater causal emergence than smaller ones, suggesting a link between competition-driven multicellularity and integrated agency (see here for more on this topic), which might have significant implications for a feedback loop up-scaling intelligence in evolution.
- These dynamics reveal the presence of not only structural features (actual boundaries between merged cells) but also physiological/behaviora/cognitive domains that do not respect (and cannot be inferred from!) the anatomical boundaries, suggesting this as a minimal model of origin and dynamics of non-physical patterns that are important targets in biomedicine, neurology, and diverse intelligence contexts.
There’s one other interesting issue to mention. We were initially puzzled by one thing: while the health of agents was steadily rising as the population developed bigger multicellular individuals, we observed a precipitous drop-off toward the end. Why? Remember that cells gain energy according to the payoff matrix of PD, and do very well as cooperative subunits of multicellular blobs. But when the blobs get big (and thus fewer in number), there are fewer others to play against, and thus, fewer and fewer opportunities to get reward! This raises a profound eschatological question about how to simulate the end of this kind of world. More broadly, what happens when a form of life and mind expands to the edges of its universe – when there is no one else to interact with because everything has merged into one pervasive being? I can think of 3 possible ways forward:
- everything dies – a sort of heat-death of the universe scenario, where the agent has consumed everything there is to consume, and thus dies.
- a cycle of fragmentation and unification – perhaps the boredom of being the only mind in a universe results in a (possibly traumatic!) fragmentation – like a human mind under great stress splitting up into personalities. (See this concept discussed by Bernardo Kastrup and Rupert Spira – that we are all fragmented alters produced by a dissociative identity process from a great cosmic universal mind). This could then lead to progressive cycles of fragmentation and unification, over and over again (a kind of Breaths of Brahma or bouncing universe model).
- breaking through into a new space – perhaps, as happens with cells gaining access to anatomical morphospace by networking into multicellularity, an agent that has achieved sufficient unity (and sufficient causal emergence) can then exert its efforts into an entirely new space, beginning the cycle of exploration (and possibly of unification with other agents who may already be there).
Future work will explore all of these questions, and link the models more tightly to biomedically-relevant policies for managing the merge-split decisions of real cells and multicellular components, as well as for detecting and reprogramming the non-anatomical, subtle patterns (of energy, information, alignment, stress, etc.) that may guide health and disease.
Featured Image by Midjourney.
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