MODEL GAME THEORY & SAPPHONS · GAME THEORY · HIDDEN TYPES · under KEEPER ERIS

Bayesian Games & Signaling

When players hold private information, they are of different types, and what they do can reveal their type. Harsanyi turned this into Bayesian games; Spence showed that costly education can signal productivity even when it teaches nothing. Both the separating and the pooling outcome can be equilibria.

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"

LIT John Harsanyi, “Games with incomplete information played by ‘Bayesian’ players”, Management Science 14:159 (1967): nature draws each player’s type from a common prior, players know their own type, and they update beliefs about others by Bayes’ rule. Nobel 1994.

LIT Michael Spence, “Job market signaling”, QJE 87:355 (1973): workers have productivity θ_L or θ_H, and education costs e/θ (cheaper for the able). A separating equilibrium needs the low type not to mimic (θ_H − e/θ_L ≤ θ_L) and the high type to want to signal (θ_H − e/θ_H ≥ θ_L), so e is in [θ_L(θ_H − θ_L), θ_H(θ_H − θ_L)]. Nobel 2001 with Akerlof and Stiglitz.

LIT Bayes’ rule: P(H | s) = P(H)·P(s | H) / [P(H)·P(s | H) + P(L)·P(s | L)].

MODEL The agents play the game reduced to two strategies each, with payoffs computed from θ = (1, 2), prior 1/2, and e = 1. The worker earns the expected wage minus cost; the employer loses the squared pay error. Both (Separate, Trust) and (Pool, Ignore) are equilibria.

AMBER Real labour markets mix signalling with human capital: education also raises productivity. Spence’s model isolates the signalling part on purpose.

MODEL Two agents, as Dave set for every world: WORKER and EMPLOYER play the Spence signaling game in normal form (MODEL payoffs) 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 {11/4} 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 WORKER ↔ EMPLOYER

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

proving…

Seal sha256(name|slug|blurb): 392b884715b407409b2837c7a7f4bc76285a495e93be1ac54ffeead226eab6c8

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