Simulation on TouchingFish.top

The Rhythm of the Game

Mon, 19 Jun 2023 00:00:00 +0000

I have written two ABMs (Agent-Based Models) before. On a grid, agents are paired at random, play one round of a game, then update their action. The only variable is "what you look at" — the payoff of this step, or the cumulative payoff across all historical games. I cannot derive the differential equations myself (the mean-field approximation was copied from the literature), but I can still follow the order of the ODEs: one is first-order, the other is second-order. Velocity versus acceleration, memoryless versus inertial. The micro-level setting is a hair's breadth apart.

The Velocity and Inertia of Evolution

Sat, 04 Feb 2023 00:00:00 +0000

I do not know the mathematics of evolutionary games, and Replicator Dynamics is just a name to me. But I do know how to run computer simulations, and the Agent-Based Model (ABM) is my language.

Suppose we have an $n \times n$ grid. Generate a population of agents by multiplying the number of cells by the population density. At each step, agents carry an action, move across the grid, find another agent in their Von Neumann neighbourhood, play a round of a classical game, then update their action and move to the next step. All agents update their action the same way. The above defines the basic elements of the model.

Starting with Yeast Cells

Tue, 15 Nov 2022 00:00:00 +0000

Yeast cells secrete invertase outside the cell wall to break down sucrose, and the digested sugar is freely available to everyone. That is what makes this interesting. A cell can choose to "cheat": use the enzymes secreted by its neighbours without secreting any itself. Researchers call yeast with a functional SUC2 gene "cooperators" and yeast with SUC2 deleted "cheaters," then pit them against each other in competition.

The results are counterintuitive:

An Angel Passes: The Phenomenon of "Spontaneous Silence" in Unsupervised Classrooms

Wed, 15 Jul 2020 00:00:00 +0000

Background

I think we can all agree on the following facts of life: an unsupervised self-study class, the moment the teacher's footsteps fade down the corridor, immediately becomes the closest thing to a livestock market that a school building has ever hosted. Then, the second those same footsteps return — never mind that the teacher is still a solid thirty seconds away and probably looking for their lanyard — the room achieves a level of collective silence usually reserved for the funerals of people we didn't much care for.