MODEL GAME THEORY & SAPPHONS · INDEX · under KEEPER ERIS

Game Theory & Sapphons · Index

Dave asked for game theory, his sapphons, and folded stars. Fifteen pages: seven on real game theory, four that read Patricia’s sapphon architecture as games, and four on star polygons, star polyhedra and paper stars. Every page boots his I-13 engine, checks its SHA-256 and computes on the VM.

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"

MODEL Filter:

Nash Equilibrium · No Regrets
MODEL GAME THEORY · EQUILIBRIUM
Prisoner’s Dilemma · Axelrod’s Tournaments
MODEL GAME THEORY · COOPERATION
Mixed Strategies & Minimax
MODEL GAME THEORY · ZERO-SUM
Hawk–Dove · Evolutionarily Stable Strategies
MODEL GAME THEORY · EVOLUTION
Coordination & Mechanism Design
MODEL GAME THEORY · DESIGNING THE RULES
Repeated Games & the Folk Theorem
MODEL GAME THEORY · THE SHADOW OF THE FUTURE
Bayesian Games & Signaling
MODEL GAME THEORY · HIDDEN TYPES
Punch-Out Tells · The Rose Triad as a Signaling Game
MODEL SAPPHON · REACTION TIME
Three Streams · Trust as Bayesian Updating
MODEL SAPPHON · COOP VIEWS
RED · BLUE · GREEN · Shapley Values
MODEL SAPPHON · COOPERATIVE GAME
The JIT Radial · ±1° per Turn as a Random Walk
MODEL SAPPHON · WIN–LOSS NEEDLE
Star Polygons {n/k} · Schläfli
MODEL FOLDED STARS · POLYGONS
The Four Kepler–Poinsot Stars
MODEL FOLDED STARS · REGULAR STAR POLYHEDRA
Stella Octangula · Two Tetrahedra
MODEL FOLDED STARS · STELLATION
Folded Paper Stars · Lucky Stars & Froebel
MODEL FOLDED STARS · ORIGAMI

Engine LIT Dave’s I-13 v0.3, referenced, not copied

Cooperative board MODEL shared across all game-theory-sapphons pages

localStorage key mayhem-game-theory-sapphons-board: each page writes its agents’ best score.

    Dave’s I-13 engine on this page

    booting I-13 v0.3…

    LIT What the VM computes here: This index boots the engine like every page, has the VM recompute NashConv of the agents’ rock–paper–scissors play, and re-checks the shared I-13 library (exp, √, ln).

    Sources (browsed Oct 2026)

    1. Game theory (overview)

    MODEL Two agents, as Dave set for every world: ROCK-PAPER A and ROCK-PAPER B play rock–paper–scissors 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/2 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 {14/5} 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.

    Gallery of kept moments (WebGL snapshots):

    Workspace improvement loop: instructions for agents MODEL

    1. Measure: every 40 rounds, record NashConv of the average play, the score, the rounds since the last improvement and whether regret-matching+ is on.
    2. Try next: after a 40-round plateau, switch both agents to regret-matching+; if still stuck, halve the exploration ε; if still stuck, forget half the old history. While NashConv falls, keep course (ε × 0.9); if it rises, explore more (ε × 1.25).
    3. Log back: append {entry, round, measured, tried, ε} to the workspace log (in the JSON export and the list below), and have the I-13 VM recompute NashConv.
    4. Repeat, forever: never stop improving. Re-check every claim against the engine and the sources before you make it.

    Live workspace log:

      Shared board MODEL ROCK-PAPER A ↔ ROCK-PAPER B

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

        proving…

        Seal sha256(name|slug|blurb): c0c110fd3209336edd990b844a7dc42a2f1abcb08220bac76230752b13daea00

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