npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
> Compositional game theory via Para/Optic structure
Formalizes cybernetic feedback loops between Agent-O-Rama off-chain agents, Worldnet bridge, and STC/Aptos on-chain settlement as GF(3) Nash equilibrium open games.
Analyzes game theory for crypto protocols, DeFi mechanisms, governance, tokenomics, MEV, auctions, and web3 incentives. Identifies exploits, equilibria, and design improvements.
Identifies strategic options and gameplay patterns from Wardley Maps for competitive advantage. Useful for planning, design guidance, and best practices.
Share bugs, ideas, or general feedback.
Compositional game theory via Para/Optic structure
Trit: 0 (ERGODIC) Color: #26D826 (Green) Role: Coordinator/Transporter
"Parametrised optics model cybernetic systems, namely dynamical systems steered by one or more agents. Then ⊛ represents agency being exerted on systems" — @bmorphism, GitHub bio
"We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models" — Compositional Game Theory, Ghani, Hedges, Winschel, Zahn (2016)
Key Papers (from bmorphism's Plurigrid references):
CyberCat Institute Connection: Open games are central to the CyberCat Institute research program on categorical cybernetics.
Related to bmorphism's work on:
Open games are morphisms in a symmetric monoidal category:
┌───────────┐
X ──→│ │──→ Y
│ Game G │
R ←──│ │←── S
└───────────┘
Where:
Para p a b = ∃m. (m, p m a → b)
-- Existential parameter with action
Optic p s t a b = ∀f. p a (f a b) → p s (f s t)
-- Profunctor optic for bidirectional data
OpenGame s t a b =
{ play : s → a
, coplay : s → b → t
, equilibrium : s → Prop
}
G ; H = Game where
play = H.play ∘ G.play
coplay = G.coplay ∘ (id × H.coplay)
G ⊗ H = Game where
play = G.play × H.play
coplay = G.coplay × H.coplay
isEquilibrium :: OpenGame s t a b → s → Bool
isEquilibrium g s =
let a = play g s
bestResponse = argmax (\a' → utility (coplay g s (respond a')))
in a == bestResponse
eq(G ; H) = eq(G) ∧ eq(H) -- under compatibility
(defn opengame-derive
"Transport game through derivation chain"
[game derivation]
(let [; Forward: strategies through derivation
forward (compose (:play game) (:forward derivation))
; Backward: utilities through co-derivation
backward (compose (:coplay game) (:backward derivation))]
{:play forward
:coplay backward
:equilibrium (transported-equilibrium game derivation)}))
temporal-coalgebra (-1) ⊗ open-games (0) ⊗ free-monad-gen (+1) = 0 ✓
three-match (-1) ⊗ open-games (0) ⊗ operad-compose (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ open-games (0) ⊗ topos-generate (+1) = 0 ✓
# Compose games sequentially
just opengame-seq G H
# Compose games in parallel
just opengame-par G H
# Check Nash equilibrium
just opengame-nash game strategy
# Transport through derivation
just opengame-derive game deriv
prisonersDilemma :: OpenGame () () (Bool, Bool) (Int, Int)
prisonersDilemma = Game {
play = \() → (Defect, Defect), -- Nash
coplay = \() (p1, p2) → payoffMatrix p1 p2
}
market :: OpenGame Price Price Quantity Quantity
market = supplyGame ⊗ demandGame
where equilibrium = supplyGame.eq ∧ demandGame.eq
OpenGame ≃ Para(Lens) ≃ Optic(→, ×)
Composition:
(A ⊸ B) ⊗ (B ⊸ C) → (A ⊸ C) -- via cut
Tensor:
(A ⊸ B) ⊗ (C ⊸ D) → (A ⊗ C ⊸ B ⊗ D)
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
game-theory: 21 citations in bib.duckdbThis skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.