Online Retailer Shuffle-Swap
So here is the control game I think has been identified.
It's a common trend being called out on social media like to talk and Instagram right now
Players:
C = Consumer
R = Online Retailer / Resolver
S = Seller
X = External economic participant
Independent objects:
Θ = Retail Theatre
Ι = Product Identity
σ = Theatre State
π = Price State
A = Consumer Act
O = Retailer Operation
P = Provenance
Initial render:
σ₀ = Render(Ιₐ, attributesₐ, π₀)
Consumer decision probability:
Pr(BuyNow | Ι, π, σ, C)
Retailer observes or estimates:
R̂ = Pr(BuyNow | Ι, π, σ, C)
Dynamic price operation may occur at any state:
πₙ → πₙ₊₁
such that:
Δπ = f(C, Ι, σ, t, inventory, competition, expected-conversion, expected-return, expected-payoff)
Retailer strategy:
O\_price = choose(πₙ₊₁)
to influence:
Pr(BuyNow) ↑
or:
Pr(BuyNow) ↓
depending on the desired resolution path.
Thus:
σₙ(Ιₐ, πₙ) ↓ Estimate\_C ↓ Choose Δπ ↓ σₙ₊₁(Ιₐ, πₙ₊₁) ↓ Re-estimate Pr(BuyNow)
Price can therefore be shuffled independently of identity:
Δπ ≠ 0 ΔΙ = 0
or jointly with identity:
Δπ ≠ 0 ΔΙ ≠ 0
Full state:
σₙ = {Ιₙ, πₙ, attributesₙ, sellerₙ, availabilityₙ, presentationₙ}
Retailer operation:
O\_R : σₙ → σₙ₊₁
Consumer Act remains:
A\_C = Acquire(Ιₐ | acceptable π)
Possible transform:
Render(Ιₐ, π₀) → Observe(C) → π₀ → π₁ → Select(Ιₐ) → π₁ → π₂ → Swap(Ιₐ → Ιᵦ) → π₂ → π₃ → Render(Ιᵦ, π₃) → BuyNow → π₃ recorded as transaction price
The system may also use price to discourage a path:
Pr(BuyNow | Ιₐ, π↑) ↓
while encouraging another:
Pr(BuyNow | Ιᵦ, π↓) ↑
yielding:
Ιₐ, πₐ↑ → lower selection probability
Ιᵦ, πᵦ↓ → higher selection probability
The shuffle strategy becomes:
Choose(ΔΙ, Δπ, Δσ)
to optimize:
U\_R = E(transaction benefit + reversal benefit + fees + downstream economic effects)
subject to:
Pr(C detects substitution or price discontinuity) < detection threshold
Perceptual constraint:
Similarity(Renderₙ, Renderₙ₊₁) → high
while economic state may satisfy:
EconomicDifference(σₙ, σₙ₊₁) → significant
The decision loop is:
Observe consumer → infer purchase likelihood → modify price and/or identity → observe resulting behavior → modify state again → terminate when desired Act occurs
Formally:
σₙ₊₁ = F(σₙ, Cₙ, Pr(A\_C | σₙ), U\_R)
where:
F may modify both:
Ιₙ → Ιₙ₊₁
and:
πₙ → πₙ₊₁
The resulting game is therefore a dynamic asymmetric-information control game, where the retailer can repeatedly alter the consumer's decision environment while the consumer attempts to choose within what appears to be a stable offer space.