Harri Ehtamo

1
On Tariff Adjustmentin a Principal Agent Game

• Harri Ehtamo
• Kimmo Berg
• Mitri Kitti

Systems Analysis Laboratory Helsinki University
of Technology www.sal.hut.fi
2
Principal-agent games

• Seller-buyer price tariff
• Manager-worker wage contract
• Taxation
• Public good (Groves mechanism, 1973)
• Auctions
• Bargaining

3
A seller-buyer game

• us (t, x) t c(x)
• ub (t, x) V(x) - t

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Solution by a linear tariff t a kx

• V(x) k c(x)
• V(x) a kx t
• Linear tariff t t c(x)(x - x)

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The linear tariff
us const.
c(x)d
V(x)
ub const.
t
d
x
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Use production cost for pricing

• t c(x) d nonlinear pricing
• t t c(x)(x - x) linear pricing

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Incomplete information high and low consumer

• qHV(x), qLV(x) V(x) known pH, pL known
• Compute BN-equilibrium directly,
• or use revelation principle
• Here VH, VL unknown gt
• use adjustment processes

8
BR-dynamics
q2
q1 r1(q2)
q21
q2 r2(q1)
q1
q10
q12
9
BR-adjustment of the linear contract
t t c(x)(x - x)
.
.
.
t
x
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Bayesian Nash equilibrium

• Highest type first
• V(qH,xH) c(xH)
• Other types in descending order Find xi
• FV(qi,xi),V(qi1,xi),c(xi)0 i 0,...,H-1

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Determining price levels
q0 first t0V(q0,x0) Other types Indifferent
to the previous bundle
ti
t0
quantities known
x0
xi
12
Optimal bundles by adjustment
adjust linear tariff
Start
quantities
prices
End
type
"take it or leave it"
Lowest
Highest

• Simple Adjustment rules with approximations