AJAE Appendix: Willingness to Pay Versus Expected Consumption Value in Vickrey Auctions for New Experience Goods

Differentiating F π, r, p, p_i, p₂ with respect to its elements

We differentiate F π, r, p, p_i, p₂ with respect to its elements π, r, a, p₁, and p₂.

— = v₂-a-p₂- v₂-va-p₂ - v₁ - p₁ 1 + r /r
δπ

(A3)    = v₂-a-p₂-v₂-va-p₂-v v_i-p_i - v₂+a-p₂ - v_i-p_i Ir,

= -2a + vɪ - p₁ - v₂ + a - p₂ / r < 0

(A4) —= ∖-π v₁-p₁- v₂-va-p₂ ∕r²<0,
δr

— = -π+ ∖-π 1 -vr Ir= l-π + r(l-2π) Ir
(A5) δa

---= π-v ∖-π 1 + r Ir= ∖-π-vr ∕r>0
(A6) δp_l

---= -π- ∖-π 1 + r lr = - ∖-π-Vr ∕r<0
(A7) δp₂

Conditions that give an optimal bid that equals the expected consumption value in an
auction for a new experience good

It is straightforward to show that ifv₁-p₁=v₂-α-p₂, v₁-p₁=v₂ +a-p₂, r = ∞, ττ = O,
π = 1, or a = 0, there would not be any information value associated with trying the new
brand in the auction, and the subgame perfect bidding strategy would be equal to the expected
consumption value.

First, if v₁ - p₁ - v₂ - a - p₂, we have that F > 0. This gives the following optimal bid from
equation (14):

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