Jose Betancourt
@jbetancourt015.bsky.social
Physics PhD student at Yale. Econ-adjacent. I’m fascinated by networks, complexity and chaos.
Perhaps the most fascinating implication of this result is that networks can discontinuously respond to changes in motif values. This is a phenomenon called “phase transitions”. This means that even a small change in parameters can populate or destroy the network!
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October 14, 2025 at 4:18 PM
Perhaps the most fascinating implication of this result is that networks can discontinuously respond to changes in motif values. This is a phenomenon called “phase transitions”. This means that even a small change in parameters can populate or destroy the network!
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I show that the motif model converges to a (directed) Erdös-Rényi model, where the density solves the optimization problem below.
It intuitively says that agents try to form structures that maximize their motif values, but it is costly to explore the vast space of networks.
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It intuitively says that agents try to form structures that maximize their motif values, but it is costly to explore the vast space of networks.
12/
October 14, 2025 at 4:18 PM
I show that the motif model converges to a (directed) Erdös-Rényi model, where the density solves the optimization problem below.
It intuitively says that agents try to form structures that maximize their motif values, but it is costly to explore the vast space of networks.
12/
It intuitively says that agents try to form structures that maximize their motif values, but it is costly to explore the vast space of networks.
12/
It could also be the case that if someone reciprocates a link, both individuals receive some benefit.
These are examples of motifs: recurring structures whose value doesn’t depend on who participates, only on the structure of connections. The examples above look like this:
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These are examples of motifs: recurring structures whose value doesn’t depend on who participates, only on the structure of connections. The examples above look like this:
10/
October 14, 2025 at 4:18 PM
It could also be the case that if someone reciprocates a link, both individuals receive some benefit.
These are examples of motifs: recurring structures whose value doesn’t depend on who participates, only on the structure of connections. The examples above look like this:
10/
These are examples of motifs: recurring structures whose value doesn’t depend on who participates, only on the structure of connections. The examples above look like this:
10/
When the game is a potential game, the stationary distribution has the following form, called a Gibbs measure. What is Φ? It’s the potential of the game!
This means that the long-run properties of the process have a clear relation to the static properties of the game.
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This means that the long-run properties of the process have a clear relation to the static properties of the game.
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October 14, 2025 at 4:18 PM
When the game is a potential game, the stationary distribution has the following form, called a Gibbs measure. What is Φ? It’s the potential of the game!
This means that the long-run properties of the process have a clear relation to the static properties of the game.
7/
This means that the long-run properties of the process have a clear relation to the static properties of the game.
7/
Adding this friendship will change how much you value the social network. You can think about your choice in two ways:
1. How would this friendship change your valuation of the whole network?
2. Which new sub-structures does this link create, and how much do you value them?
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1. How would this friendship change your valuation of the whole network?
2. Which new sub-structures does this link create, and how much do you value them?
3/
October 14, 2025 at 4:18 PM
Adding this friendship will change how much you value the social network. You can think about your choice in two ways:
1. How would this friendship change your valuation of the whole network?
2. Which new sub-structures does this link create, and how much do you value them?
3/
1. How would this friendship change your valuation of the whole network?
2. Which new sub-structures does this link create, and how much do you value them?
3/
Networks are fluid objects. Regardless of the application you’re interested in, chances are links are being created and destroyed all the time.
Let’s think about your social network. You might bump into someone new and think about whether you want to be their friend.
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Let’s think about your social network. You might bump into someone new and think about whether you want to be their friend.
2/
October 14, 2025 at 4:18 PM
Networks are fluid objects. Regardless of the application you’re interested in, chances are links are being created and destroyed all the time.
Let’s think about your social network. You might bump into someone new and think about whether you want to be their friend.
2/
Let’s think about your social network. You might bump into someone new and think about whether you want to be their friend.
2/
New working paper!
Have you ever wondered how the way you form friendships, partnerships, etc affects the structure of how society as a whole interacts?
It turns out that even small changes to individual incentives can have huge aggregate effects!
A 🧵:
Have you ever wondered how the way you form friendships, partnerships, etc affects the structure of how society as a whole interacts?
It turns out that even small changes to individual incentives can have huge aggregate effects!
A 🧵:
October 14, 2025 at 4:18 PM
New working paper!
Have you ever wondered how the way you form friendships, partnerships, etc affects the structure of how society as a whole interacts?
It turns out that even small changes to individual incentives can have huge aggregate effects!
A 🧵:
Have you ever wondered how the way you form friendships, partnerships, etc affects the structure of how society as a whole interacts?
It turns out that even small changes to individual incentives can have huge aggregate effects!
A 🧵: