The Landscape in 3D

A world of policies is a landscape, and its ruggedness is a dial. Turn K up and watch a smooth hill fracture into a field of traps. Drag to rotate.


Building…
How many other policies each policy leans on. Same genotypes, re-scored.
Genome length — the dimension of the world being flattened.
How many genotypes are sampled onto the grid.

What you're looking at

Every point on this surface is one complete set of policies — a genome. Its height (and colour) is its fitness. The trick, borrowed straight from the source notebook, is the flat plane: a 16-dimensional space of 65,536 possible genomes can't be drawn, so a patch of it is sampled and laid on a grid such that neighbouring points differ by only a bit or two — plotted in Hamming space. Nearby on the grid means nearby in genome.

Now turn K. At K = 0 each policy's contribution is independent, so the landscape is a single smooth hill — easy to climb, one best answer. As K rises, each policy's payoff depends on more of the others, and the surface shatters into peaks and valleys: many places to be locally optimal yet globally mediocre. That ruggedness is the difficulty of the world, and it's the same picture the white paper's Figure 2 shows as four still frames — here you can rotate it and slide K yourself.

This is a single, uncoupled NK landscape (the C — coupling between countries — is what makes the full game; run that here). The method and code are Mathew Best's, at github.com/matbest/LLMJupyterTester.