MODEL GAME THEORY & SAPPHONS · SAPPHON · COOPERATIVE GAME · under KEEPER ERIS

RED · BLUE · GREEN · Shapley Values

Dave’s four-sapphon radial: RED (what happens to Patricia, and memory), BLUE (how to respond), GREEN (was it successful), with Patricia’s amethyst core making the final call. Treat the three as a coalition: how much of a good turn does each deserve? Shapley’s 1953 value answers that, and the I-13 VM computes it.

Dave (t252): "i love that set up can you build some pages looking into game theory and those sappons you just built, see if you can build some folded stars and stuff"

Dave (t248, NES Agents app): "i love it but there need to be 3 sappons togeterh , do 1 red, what happens to patricia and how remember it, blue, how you respond to what happens. and green , was it successfuel. so have one sapphone radi with 4 sapphones in it and then the jit engines running cocurrently together"

Dave (t247, NES Agents app): "no engine, did you upgraed it or no, how about a whole rebuild from the ground up with everything leargned and the new jit engine with patricia, purple sapphone amethys core"

LIT Lloyd Shapley, “A value for n-person games” (Contributions to the Theory of Games II, 1953, pp. 307–317): average each player’s marginal contribution v(S ∪ i) − v(S) over all orders in which the coalition could form. It is the only rule that is efficient, symmetric, additive and gives null players 0. Shapley shared the 2012 Nobel with Roth.

LIT The core: splits that give every sub-coalition at least what it could get alone. In convex games the Shapley value is always in the core.

MODEL Characteristic function (sliders): v(RED) 1, v(BLUE) 2, v(GREEN) 0.5, v(RED+BLUE) 5, v(RED+GREEN) 2.5, v(BLUE+GREEN) 3.5, v(all) 8, read as how much of a successful turn each team of sapphons produces. PATRICIA’s blend weights are taken as Shapley value / v(all). These numbers are mine, not measured in v43.

MODEL The agents are BLUE and GREEN in an inspection game: BLUE can be careful or hasty, GREEN can check or trust. GREEN checks with probability 1/3 and BLUE is hasty 1/4 of the time in equilibrium.

MODEL Two agents, as Dave set for every world: BLUE and GREEN play the BLUE–GREEN inspection game (MODEL) over and over by regret matching (Hart & Mas-Colell 2000), each shifting toward the moves it regrets not having played. Their score is 1 − NashConv/3 of their empirical average play (1 = an exact Nash equilibrium), and the I-13 VM re-computes NashConv from the raw averages every time the score improves. The centrepiece is a folded star {13/5} whose fold rises with the score. Three.js r160 from a pinned CDN, devicePixelRatio capped at 2. Drag to orbit, scroll to zoom.

LIT on load: the seal is recomputed, the page’s facts are re-checked as arithmetic (throws on mismatch), 200 seeded rounds of the two agents must improve their score, the workspace loop logs 5 entries, and the OBJ and SVG exports must be consistent. Then the engine boots, its SHA-256 and regression lab are checked, the VM recomputes the agents’ NashConv, and the page’s VM results are compared with independent JS.

⏸ Pause Reseed Export training + workspace log (.json) Export star + trajectory (.svg) Export folded star (.obj)

Gallery of kept moments (WebGL snapshots):

Shared board MODEL BLUE ↔ GREEN

Background art: MODEL a generative field seeded from this page’s seal.

proving…

Seal sha256(name|slug|blurb): d8f1d304e5b3223dbb60d9e3e1104e88cf433ef6c359ea10975d59198f37a718

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