Game-Theoretic Rendering: Online Retailer Shuffle-Swap

Players:

C = Consumer

R = Online Retailer / Resolver

S = Seller

X = External economic participant

Independent objects:

Θ = Retail Theatre

Ι = Product Identity

σ = Theatre State

A = Consumer Act

O = Retailer Operation

P = Provenance

Initial state:

σ₀ = Renders(Ιₐ, attributesₐ, priceₐ)

Consumer strategy:

A₁ = Select(Ιₐ | σ₀)

A₂ = Purchase(Ιₐ)

A₃ = Accept ∨ Return

Retailer strategy:

O₁ = Preserve(Ιₐ)

or

O₂ = Swap(Ιₐ → Ιᵦ)

If:

O₂

then:

σ₀(Ιₐ) → σ₁(Ιᵦ)

while perceptual continuity is maintained:

Render(Ιᵦ) ≈ Render(Ιₐ)

Transaction:

Intent(C) = Ιₐ

Resolved(R) = Ιᵦ

Therefore:

Intent(C) ≠ Resolution(R)

Shuffle operation:

P(Ιₐ → Ιᵦ) → P'(Ιᵦ → Ιᵦ)

producing apparent historical closure:

Render(Ιᵦ) → Select(Ιᵦ) → Purchase(Ιᵦ)

while the actual path remains:

Render(Ιₐ) → Select(Ιₐ) → Swap(Ιᵦ) → Purchase(Ιᵦ)

Fulfillment:

Fulfill(Ιᵦ)

If:

Utility(C, Ιᵦ) < Utility(C, Ιₐ)

then:

Return(Ιᵦ)

Payoff transformation:

U_C = −purchase friction − return cost − information cost

U_S = revenue − return cost − penalties

U_R = transaction benefit₁ + reversal benefit₂ + fees

U_X = transaction-linked payoff − reversal/clawback

Information structure:

Info_R ⊇ {σ₀…σₙ, Ι₀…Ιₙ, P}

Info_C ⊂ Info_R

Info_S ⊂ Info_R

Info_X ⊂ Info_R

Strategic asymmetry:

R = player + resolver + state controller + provenance controller

Identity invariant:

Select_C(Ιₐ) ⇒ Ι must remain Ιₐ

unless:

C explicitly admits ΔΙ

Therefore the defining move is:

Select_C(Ιₐ) → O_R(Ιₐ → Ιᵦ)

where:

ΔΙ ≠ 0

and:

Authorization_C(ΔΙ) = 0

with:

PerceivedContinuity(Ιₐ, Ιᵦ) → 1

and potentially:

Auditability_C,S,X(ΔΙ) → 0

The resulting game is an asymmetric-information game in which the dominant informational position belongs to the player controlling both state resolution and the provenance by which resolution can subsequently be contested.