MODEL GAME THEORY & SAPPHONS · GAME THEORY · DESIGNING THE RULES · under KEEPER ERIS

Coordination & Mechanism Design

In a coordination game everyone wants to match, but there can be several equilibria: hunt the stag together, or each take a safe hare. Mechanism design runs the other way: choose the rules so selfish play gives the outcome you want. Vickrey’s second-price auction makes honest bidding optimal.

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’s I-13 engine on this page

booting I-13 v0.3…

LIT What the VM computes here: For every auction the VM finds the highest and second-highest of the n values with if-chains, and adds up both formats’ revenue (second price; (n − 1)/n × highest). It computes (n − 1)/(n + 1) too. It also computes the Stag Hunt expected payoffs. JS only draws the random values.

LIT Stag Hunt (Rousseau’s parable): (Stag, Stag) pays 4 each, a hare pays 3 whatever the partner does, and a lone stag hunter gets 0. Both (Stag, Stag) and (Hare, Hare) are equilibria. Harsanyi & Selten (1988) call Stag payoff-dominant and Hare risk-dominant, since the product of deviation losses is (3 − 0)² = 9 for Hare versus (4 − 3)² = 1 for Stag. Hunt stag only if you think your partner will with probability ≥ 3/4.

LIT Thomas Schelling, The Strategy of Conflict (1960): people often coordinate on focal points, choices that stand out, without communicating. Schelling shared the 2005 Nobel with Aumann.

LIT William Vickrey, J Finance 16:8 (1961): in a sealed-bid second-price auction, bidding your true value is weakly dominant. Revenue equivalence (Vickrey 1961; Myerson 1981): with n bidders whose values are independent and uniform on [0, 1], the first-price (equilibrium bid (n − 1)v/n) and second-price formats both earn (n − 1)/(n + 1) on average.

LIT Hurwicz, Maskin and Myerson won the 2007 Nobel for laying the foundations of mechanism design.

MODEL Auction values are drawn by JS’s seeded generator and passed to the VM as literals. The theory line is exact; the simulated averages wobble with the sample.

Lab MODEL interactive, computed on the I-13 VM

bidders n · auctions

Stag Hunt: P(partner hunts stag)

Sources (browsed Oct 2026)

  1. Vickrey (1961) Counterspeculation, auctions, and competitive sealed tenders, J Finance 16:8
  2. Myerson (1981) Optimal auction design, Math Oper Res 6:58
  3. Nobel 2005 scientific background (Aumann, Schelling)
  4. Lindau: game theory Nobel laureates (2007 mechanism design)

MODEL Two agents, as Dave set for every world: HUNTER A and HUNTER B play the Stag Hunt 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/4 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 {10/3} 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 HUNTER A ↔ HUNTER B

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

      proving…

      Seal sha256(name|slug|blurb): 47c57bf8ed45a7c15a996001f119b9a1c39efb3e092a3851dd7996fd3736737c

      ↑ Game Theory & Sapphons index · Protein Folding (same engine) · ← ERIS, keeper of Mayhem