Master-Thesis 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.

When the Commons Starts to Breathe

Thu, 15 Jun 2023 00:00:00 +0000

The tragedy of the commons is an old story.

In 1968, Garrett Hardin described a scene like this: an open pasture that anyone can graze, with every herder adding one more cow of their own. The benefit of that extra cow accrues entirely to the herder, while the cost of pasture degradation is shared by everyone. So every herder chooses to add one more, and the pasture is eventually destroyed.

Instantaneous Selection and Historical Selection

Thu, 09 Mar 2023 00:00:00 +0000

Consider a simple Agent-Based Model (ABM). On a grid, a group of agents each carry an action (strategy) and move randomly; at each step, they pair up with a neighbour, play a round of a game, receive a payoff, then update their action. The update rule is straightforward — look at the neighbours' scores, and in the next step switch to the strategy with the higher score.

There is only one key variable: which score do you compare?

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 secrete invertase outside the cell to digest sucrose, and the digested sugar is shared by everyone—and this is where it gets interesting. A cell can choose to "cheat": ride on the enzymes its neighbors secrete, while secreting none of its own. Researchers call yeast with a functional SUC2 gene "cooperators," and yeast with SUC2 deleted "cheaters," then put the two in competition.

The results are counterintuitive:

In sparse populations (low social density), cheaters have a fitness of only 0.87—worse than cooperators.
In dense populations (high social density), cheaters have a fitness as high as 1.19—better than cooperators.

Why? The higher the social density, the more likely a cooperator is to meet other cooperators. When everyone secretes enzymes together, the public pool grows, and everyone's payoff is high. But then cheaters slip in, enjoying the public goods unilaterally while paying no cost, and their payoff explodes.