A Simulation of Social Groups Under A Gift Economy

Mira Kennard

Introduction

I enjoy reading about people. Not individuals, but rather cultures, empires, kinship groups, etc. I'm fascinated by the emergent properties of multi-person systems. This post is born out of love for my favorite book: "Stone Age Economics" by Marshall Sahlins. In this text Sahlins elaborates on the economic life of hunter-gatherer and simple agricultural societies which exist today, extrapolating this into the past. He touches on many different points, but the one this post will focus on is the concept of debt and gift-economies as the progenitor to our modern economic system.

If you were taught the Smithian notion of the historical existence of barter economies, I'm sorry to say that you were taught wrong, or at least were taught a long while back. To quote Humphrey, Caroline. 1985. "Barter and Economic Disintegration.":

"No example of a barter economy,pure and simple,has ever been described,let alone the emergence from it of money;all available ethnography suggests that there never has been such a thing."

If the idea of traders exchanging goods in a marketplace without currency is mostly a fiction, then what *did* come before currency? In short, the gift economy: a system of mentally tabulated debts sourced from gift-giving over a small social network. Imagine you and a few friends are transported back in time. You get up, dust yourself off, and see no buildings, no roads, no crowds of people. Rather, it's simply wilderness. How should you and your friends survive and distribute resources?

You could grab something nearby, say a shiny quartz pebble and say to your friends:

"Okay, this is our currency. If you want something from me give me quartz pebbles in payment and I'll do the same for you."

But why bother? You only have a finite number of friends, and it's pretty simple to keep track of who's doing their fair share in making sure your small band survives. If you notice one of your friends napping while the rest of you are off hunting you will make note that this friend isn't a reliable partner, and you'll be less inclined to rely on this person and in turn will presumably share less of what you have with them.

This is the principle of the gift economy. Those who contribute to the small social band are more likely to later receive contributions from the social band. People keep a mental tabulation on who has contributed to their survival, resulting in this person pouring more of their resources into those who have successfully contributed. This is the progenitor to currency, not barter

I propose this principle extends into modern times, just not on the scale of entire economy. Rather gift economics form a social medium for which people interact with each other. Gift economics isn't just to be applied to ancient peoples, but modern peoples as well. In my opinion this is the fabric that binds society together at the molecular level, forming the small social groups we are all a part of.

Admittedly I base this on the anecdotal evidence of engaging with people under the premise of gift exchange for the last few years. Since reading "Stone Age Economics", whenever I find myself in a new situation with new people, I pick out the person I'd most like to get along with and give them a 'gift'. This could be anything

A favor
Candy
Caffeinated Beverages
Instant Ramen
etc

As long as someone doesn't despise the sight of me, I can usually get them to be my friend with a simple unprompted gesture of goodwill. I'd estimate that I also get a return gift ~90% of the time.

A Model of A Gift Economy

There are already plenty of models for modelling social structures, usually based around the 'hypergraph', i.e. a collection of smaller social groups within the larger structure. [https://arxiv.org/abs/2102.06825][https://arxiv.org/abs/2203.12189][ https://arxiv.org/abs/2408.13336]

In this post we will take a different approach. Instead of considering fixed or even dynamic hypergraphs, we will instead produce the hypergraph as an emergent property by assuming a probability distribution over the space of all hyperedges. There is a tradeoff with this approach however, as with a fixed hypergraph you can scale the number of people/nodes quite high. But with our framework, studying social groups first not people, there is a significant computational bottleneck when trying to scale the number of people: a result of combinatorial explosion.

Here's the github repo:

[ https://github.com/orthogonaltohumanity/gift_econ_sim/tree/main ]

Assume you have people who can form social groups. Let the set of all social groups person is in be Then for each person at time we have two maps

represents person $n$'s opinion of social group at time . This is equivalent to the probability the person interacts with with group .

represents the sum total of all gifts person has given group .

Then we uniformly sample an agent. Then sample a group according to the distribution generated by over . One more sample (the amount of gifted labor power taken/given to a group) and we update according to the rule

and then for such that we update

And that's it. You can vary the '2' if you want but we keep it fixed for our simulations. This is an area for future work.

Results

We take 7 agents starting with a uniform choice distribution over social groups and iterate the model for 10,000 timesteps. The following image is a scatter plot of social groups plotted by their average opinion vs the sum of gifts which have been given/taken from the group.

Notice how only a few social structures are active at any given time. If we restrict the social groups we look at to those with average probability across agents greater than we get a hypergraph with a analyzable number of hyperedges.

This is what the emergent social structures look like represented as a hypergraph.

I recently read Samuel Arbesman’s "The Life-Spans of Empires", a short paper fitting an exponential distribution to the distribution of empire lifespans. His result was very striking, as the exponential distribution fit very well to his 41 empire examples as shown below.

Screenshot 2026-05-01 at 12-44-13 The Life-Spans of Empires - arbesman2011a.pdf.png

After an hour of staring at the above hypergraph gif I realized the same logic could be applied to our social groups. We could ask:

Whats the distribution of timespans between different hypergraph configurations, i.e. whats the decay rate of the composition of society as a whole?
Whats the distribution of lifetimes of single hyperedges, i.e. whats the decay rate of social groups?

So we plot and get:

Linear on the log-log so it's a power law. Not the same result as Arbesman. However 41 is a small sample size. We can do better. It was at this point I turned to Opus 4.7 and asked it to find a larger dataset, which it did in Cliopatria: "a comprehensive open-source geospatial dataset of worldwide polities from 3400BCE to 2024CE". We can discard the geospatial aspect and focus only on lifetimes. What result do we get when we vibe-code an expansion to Arbesman's original work? [https://github.com/orthogonaltohumanity/culture_lifetimes]

Not exponential! Rather the data best fits a log-normal distribution better than either power or exponential distributions. This suggests societal changes happen due to some kind of series of multiplicative factors, rather than a constant hazard rate. This data contrasts with both Arbesman's original paper and our model, and this may be due to any number of factors

Arbesman specifically looks at "large empires" while the Cliopatria dataset is polities in general.
We are working with small social groups, not cultures in general
We only use 7 agents. Real cultures consist of more than 7 people.

Conclusion

There is more work to be done of course. Larger simulations, better analysis, more complex interaction options etc. I'm not sure if I'll continue this or not as I tend to be a bit distractable, but I think I have enough interest in this project to keep it going for at least a week, maybe more.

I think the next thing that should be worked on is some kind of resource constraint. Perhaps we can draw from classical economics and use the Labor Theory of Value as the baseline unit for all gifts and resources. Maybe each group (including the singletons) can have a resource pool agents can take or contribute to. I'll start working on it and we'll see what happens.

Let me know what you think, as I'd very much welcome some input. What am I missing or leaving out?

Great post! Some extensions I'd be interested in:

Model multiple different resources / specializations, perhaps with a space of skillsets / resource distributions, and everyone getting a random ~unit vector in said space (maybe even with nonuniform distribution on direction to model some skills / resources being more scarce than others). This would probably need an N that's a bit larger, but I think it would be cool to see groups forming and selecting people based on their niches. Could be an extension of the "resource pool" thing, with multiple types of resources.
Introduce a maximum group size (or perhaps simply have starting opinion decrease monotonically with group size), to help deal with the combinatorial explosion and to model the fact that humans don't really keep track of most of the large possible groups of people.
Similar to the point above, you could sort of "clamp" the probability distribution by only sampling from the top n highest-opinion groups for each given person (i.e. if my opinions are [0.01, 0.5, 0.21, 0.07, 0.32] and n=3 then I sample as if it's [0, 0.5, 0.21, 0, 0.32]. Idk if this operation has a name. It's probably similar in effect to softmax but computationally easier). This is probably more accurate to what actual humans do: we can have opinions of really large groups, like Google or the Democratic Party, but there is a (soft) maximum total number of groups we can have opinions of, due to memory and computation constraints.
Make the opinions bidirectional: groups have opinions of all of their members, add them to the set uniformly sampled over, and then the is drawn from [0, 1], to better model that, in general, entities give more to entities that they have a higher opinion of. Obviously this will make the computation take quite a bit longer. Maybe have the sampling massively down-weight bigger groups, or perhaps make it based on the average opinions of groups. You could perhaps do this elegantly by making each time step contain two actions: first, a random person contributes to a random group they are part of, sampled based on the person's opinions. Then, samples a random member based on its opinions, and gives them a random contribution. This will multiply simulation time by a factor of two but will perhaps give more interesting results!

I think even just increasing N is likely to yield some interesting results. Some galaxy-brained parallelization (maybe using the GPU?) can probably be done to make this more feasible (I haven't looked at your code yet, so if you're already doing something like this, massive props to you. I have ~no idea where I'd even start on that besides "ask Claude").

P.S. There are some minor typographical errors, including a link that doesn't link and some that doesn't render. I've marked them using reactions.

Great post! Some extensions I'd be interested in:

Model multiple different resources / specializations, perhaps with a space of skillsets / resource distributions, and everyone getting a random ~unit vector in said space (maybe even with nonuniform distribution on direction to model some skills / resources being more scarce than others). This would probably need an N that's a bit larger, but I think it would be cool to see groups forming and selecting people based on their niches. Could be an extension of the "resource pool" thing, with multiple types of resources.
Introduce a maximum group size (or perhaps simply have starting opinion decrease monotonically with group size), to help deal with the combinatorial explosion and to model the fact that humans don't really keep track of most of the large possible groups of people.
Similar to the point above, you could sort of "clamp" the probability distribution by only sampling from the top n highest-opinion groups for each given person (i.e. if my opinions are [0.01, 0.5, 0.21, 0.07, 0.32] and n=3 then I sample as if it's [0, 0.5, 0.21, 0, 0.32]. Idk if this operation has a name. It's probably similar in effect to softmax but computationally easier). This is probably more accurate to what actual humans do: we can have opinions of really large groups, like Google or the Democratic Party, but there is a (soft) maximum total number of groups we can have opinions of, due to memory and computation constraints.
Make the opinions bidirectional: groups have opinions of all of their members, add them to the set uniformly sampled over, and then the is drawn from [0, 1], to better model that, in general, entities give more to entities that they have a higher opinion of. Obviously this will make the computation take quite a bit longer. Maybe have the sampling massively down-weight bigger groups, or perhaps make it based on the average opinions of groups. You could perhaps do this elegantly by making each time step contain two actions: first, a random person contributes to a random group they are part of, sampled based on the person's opinions. Then, samples a random member based on its opinions, and gives them a random contribution. This will multiply simulation time by a factor of two but will perhaps give more interesting results!

P.S. There are some minor typographical errors, including a link that doesn't link and some that doesn't render. I've marked them using reactions.