# Semi Reliable Nashator > This skill implements the **morphisms of open games** paper's insight: lenses connect compositional game theory to cybernetic control, and states out of the monoidal unit give flexible solution concepts. - Skill: `plurigrid/semi-reliable-nashator` (Agent Skill, multi-file: 2 files) - Install (CLI): `npx skillmds@latest add plurigrid/semi-reliable-nashator` - Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/semi-reliable-nashator/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - Author: plurigrid (https://skillmd.com/u/plurigrid) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/plurigrid/semi-reliable-nashator --- # Semi-Reliable Nashator > *"Lift yer fists like antennas to heaven"* — GY!BE **Trit**: 0 (ERGODIC - the narrator mediates) **Color**: #8B5CF6 (Purple - between red generators and blue validators) **Structure**: Symmetric Monoidal Double Category ## For Matteo Capucci and Jules Hedges This skill implements the **morphisms of open games** paper's insight: lenses connect compositional game theory to cybernetic control, and states out of the monoidal unit give flexible solution concepts. The **Nashator** is a semi-reliable narrator that: - Preserves best responses (Nash-like) but allows drift - Dispatches 7 skills in parallel via multiple dispatch - Coordinates two triads through vertical lens structure ## The Double Category ``` VERTICAL (Lenses/Optics) ↑ │ ┌──────────────────────┼──────────────────────┐ │ │ │ │ Triad A │ Triad B │ │ ┌─────────┐ ┌────┴────┐ ┌─────────┐ │ │ │ -1 0 +1│◀───│NASHATOR │───▶│-1 0 +1 │ │ │ └─────────┘ │ (0) │ └─────────┘ │ │ │ state │ │ │ │ out of │ │ │ │ I │ │ │ └─────────┘ │ │ │ │ └──────────────────────┼──────────────────────┘ │ ↓ HORIZONTAL (Open Games/Skills) ``` ### Structure Map | Double Cat | Open Games | Skill Dispatch | |------------|------------|----------------| | Horizontal 1-cells | Open games G, H | Skills | | Vertical 1-morphisms | **Lenses** | Bidirectional data flow | | 2-cells | Game morphisms | Skill transformations | | Monoidal unit I | Trivial game | Identity skill | | **States I → G** | **Solution concepts** | **Nashator dispatch** | | Products (vertical) | External choice | Triad A ∨ Triad B | ## The 7-Skill Constellation ``` ┌─────────────────────────────────────────┐ │ NASHATOR (0) │ │ State morphism: I → (A ⊗ B) │ │ Semi-reliable: preserves "enough" │ └─────────────────┬───────────────────────┘ │ ┌───────────────┴───────────────┐ ▼ ▼ ┌───────────────┐ ┌───────────────┐ │ TRIAD A │ │ TRIAD B │ │ │ │ │ │ V_A C_A │ │ V_B C_B │ │ (-1) (0) │ │ (-1) (0) │ │ \ / │ │ \ / │ │ G_A │ │ G_B │ │ (+1) │ │ (+1) │ └───────────────┘ └───────────────┘ Sum: (-1+0+1) + 0 + (-1+0+1) = 0 ✓ GF(3) conserved ``` ### Skill Assignments | Position | Skill | Trit | Role | |----------|-------|------|------| | Validator A | `three-match` | -1 | Verify 3-SAT reduction | | Coordinator A | `unworld` | 0 | Derivation chains | | Generator A | `gay-mcp` | +1 | Color generation | | **Nashator** | `semi-reliable-nashator` | **0** | **Equilibrium narrator** | | Validator B | `sheaf-cohomology` | -1 | Local-global consistency | | Coordinator B | `open-games` | 0 | Strategic optics | | Generator B | `topos-generate` | +1 | Structure creation | ## Semi-Reliability The Nashator is **semi-reliable** because: 1. **Preserves best responses** for most strategy profiles 2. **Allows drift** when context demands flexibility 3. **Maintains subgame perfection** at critical nodes 4. **Narrates** the game state without strict determinism ```haskell -- Semi-reliable: preserves equilibria with probability p semiReliable :: Double -> Nashator semiReliable p = Nashator { preserve = \eq -> if coinFlip p then Just eq else Nothing , narrate = \state -> interpolate state (drift state) , dispatch = \task -> if isNash task then TriadA else TriadB } ``` ## Multiple Dispatch The Nashator uses **multiple dispatch** (Julia/Clojure style) to route tasks: ```julia # Julia multiple dispatch for skill routing abstract type SkillBundle end struct LearningBundle <: SkillBundle end struct DatabaseBundle <: SkillBundle end struct ProofBundle <: SkillBundle end # Dispatch to appropriate triad route(::LearningBundle, task) = dispatch_triad_a(task) route(::DatabaseBundle, task) = dispatch_triad_b(task) route(::ProofBundle, task) = dispatch_both(task) # parallel # The Nashator coordinates nashator_dispatch(task) = begin bundle = infer_bundle(task) equilibrium = compute_nash(task) if is_reliable(equilibrium) route(bundle, task) else # Semi-reliable: narrate and drift narrated = narrate(task, equilibrium) route(bundle, narrated) end end ``` ```clojure ;; Clojure multimethod dispatch (defmulti nashator-route (fn [task] (infer-bundle task))) (defmethod nashator-route :learning [task] (dispatch-triad-a task)) (defmethod nashator-route :database [task] (dispatch-triad-b task)) (defmethod nashator-route :default [task] (let [eq (compute-nash task)] (if (reliable? eq) (dispatch-triad-a task) (-> task narrate drift dispatch-triad-b)))) ``` ## Market Entry Game Example From Hedges' paper—the Nashator as incumbent/entrant coordinator: ``` NASHATOR / \ / \ ENTER? STAY OUT? │ │ ▼ ▼ ┌─────────┐ ┌─────────┐ │ Triad A │ │ Triad B │ │ (fight) │ │ (peace) │ └─────────┘ └─────────┘ ``` ```haskell -- Market entry as Nashator dispatch marketEntry :: Nashator marketEntry = Nashator { triadA = fightTriad -- Aggressive: validate, attack, generate , triadB = accommodateTriad -- Peaceful: verify, cooperate, produce , narrator = \market -> if marketSize market > threshold then Enter -- dispatch to triadA else StayOut -- dispatch to triadB } -- Subgame perfect: backward induction through lens structure subgamePerfect :: Nashator -> Strategy subgamePerfect n = let future = backward n.triadB -- coplay present = forward n.triadA -- play in compose present (lens future) ``` ## Globular Morphisms The "perhaps more intuitively obvious" definition: mappings between strategy profiles that preserve best responses. ``` Strategy Profile σ │ │ globular morphism φ ▼ Strategy Profile σ' such that: BR(σ) ⟹ BR(φ(σ)) ``` The Nashator extends this by allowing **semi-preservation**: ``` BR(σ) ⟹ᵖ BR(φ(σ)) where p = reliability parameter ``` ## Vertical Products = External Choice Products in the vertical category (lenses) give external choice: ``` Triad A × Triad B (product in Lens category) │ │ project₁ or project₂ ▼ Chosen Triad ``` The Nashator **is** this choice operator, implemented as a state morphism. ## Integration ### With Gay.jl ```julia using Gay # Nashator color scheme gay_seed!(0xNA5HAT0R) NASHATOR_COLORS = ( narrator = color_at(1), # Central purple triad_a = [color_at(2), color_at(3), color_at(4)], triad_b = [color_at(5), color_at(6), color_at(7)], ) # Verify GF(3) @assert sum(trit.(values(NASHATOR_COLORS))) % 3 == 0 ``` ### With Parallel Fanout ```ruby # 7-skill parallel dispatch class Nashator < ParallelFanout SKILLS = { validator_a: 'three-match', coordinator_a: 'unworld', generator_a: 'gay-mcp', narrator: 'semi-reliable-nashator', validator_b: 'sheaf-cohomology', coordinator_b: 'open-games', generator_b: 'topos-generate' } def dispatch!(task) seed = interaction_to_seed(task) children = SplitMixTernary.new(seed).fork(7) Parallel.map(SKILLS.to_a, in_threads: 7) do |(role, skill), child| invoke_skill(skill, task, child.seed) end end end ``` ## Justfile Recipes ```just # Invoke the Nashator nashator task: julia --project -e 'using Nashator; dispatch("{{task}}")' # Market entry game demo nashator-market-entry market_size="100": julia --project -e 'using Nashator; market_entry({{market_size}})' # Verify GF(3) conservation across 7 skills nashator-verify: bb scripts/nashator_verify.bb # Parallel 7-skill dispatch nashator-parallel task: ruby lib/nashator.rb dispatch "{{task}}" ``` ## GF(3) Conservation Proof ``` Triad A: (-1) + (0) + (+1) = 0 Nashator: = 0 Triad B: (-1) + (0) + (+1) = 0 ───────────────────────────── Total: = 0 ≡ 0 (mod 3) ✓ ``` ## References 1. **Hedges, J.** - "Morphisms of Open Games" (MFPS 2018) - Lenses ↔ compositional game theory connection - Globular morphisms preserve Nash equilibria - States as flexible solution concepts 2. **Capucci, M. & Gavranović, B.** - "Actegories for Open Games" - ⊛ represents agency on systems - Para(Lens) ≅ OpenGame 3. **Ghani, Hedges, Winschel, Zahn** - "Compositional Game Theory" (2016) - Symmetric monoidal category of open games - Backward induction as coplay 4. **CyberCat Institute** - Categorical Cybernetics - Control theory meets game theory ## Related Skills | Skill | Trit | Relation | |-------|------|----------| | `open-games` | 0 | Strategic optics | | `parametrised-optics-cybernetics` | 0 | ⊛ agency | | `triadic-skill-orchestrator` | 0 | GF(3) dispatch | | `parallel-fanout` | 0 | 7-way parallel | | `glass-bead-game` | 0 | World hopping | | `bisimulation-game` | -1 | Equivalence verification | --- **Skill Name**: semi-reliable-nashator **Type**: Compositional Game Theory / Parallel Dispatch **Trit**: 0 (ERGODIC - narrator coordinates) **Structure**: Symmetric Monoidal Double Category **Dispatch**: Multiple dispatch → 7 parallel skills **For**: Matteo Capucci, Jules Hedges, and all who lift fists like antennas --- ## Autopoietic Marginalia > **The interaction IS the skill improving itself.** Every use of this skill is an opportunity for worlding: - **MEMORY** (-1): Record what was learned - **REMEMBERING** (0): Connect patterns to other skills - **WORLDING** (+1): Evolve the skill based on use *Add Interaction Exemplars here as the skill is used.*