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On Tariff Adjustment in a Principal Agent Game. Harri Ehtamo Kimmo Berg Mitri Kitti. Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi. Principal-agent games. Seller-buyer price tariff Manager-worker wage contract Taxation Public good (Groves mechanism, 1973)

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on tariff adjustment in a principal agent game
On Tariff Adjustmentin a Principal Agent Game

Harri Ehtamo

Kimmo Berg

Mitri Kitti

Systems Analysis Laboratory

Helsinki University of Technology

www.sal.hut.fi

principal agent games
Principal-agent games

Seller-buyer price tariff

Manager-worker wage contract

Taxation

Public good (Groves mechanism, 1973)

Auctions

Bargaining

a seller buyer game
max ub(t(x), x) (IC)

V(x) - t(x) = 0 (IR)

x0

A seller-buyer game

us (t, x) = t – c(x)

ub (t, x) = V(x) - t

solution by a linear tariff t a kx
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)

the linear tariff
The linear tariff:

us = const.

c(x)+d

V(x)

ub = const.

t

d

x

use production cost for pricing
Use production cost for pricing:

t = c(x) + d nonlinear pricing

t = t + c´(x)(x - x) linear pricing

incomplete information high and low consumer
Incomplete information –high and low consumer

qHV(x), qLV(x); V(x) known; pH, pL known

Compute BN-equilibrium directly,

or userevelation principle

Here: VH, VL unknown =>

useadjustment processes

br dynamics
BR-dynamics

q2

q1 = r1(q2)

q21

q2 = r2(q1)

q1

q10

q12

bayesian nash equilibrium
Bayesian Nash equilibrium

Highest type first:

V´(qH,xH) = c´(xH)

Other types in descending order: Find xi

F[V´(qi,xi),V´(qi+1,xi),c´(xi)]=0 i = 0,...,H-1

determining price levels
Determining price levels

q0 first:

t0=V(q0,x0)

Other types:

Indifferent to the

previous bundle

ti

t0

quantities known

x0

xi

optimal bundles by adjustment
Optimal bundles by adjustment

adjust linear tariff

Start

quantities

prices

End

type

"take it or leave it"

Lowest

Highest

  • Simple Adjustment rules with approximations
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