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On Tariff Adjustment in a Principal Agent Game

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

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  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. 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

  4. 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)

  5. The linear tariff: us = const. c(x)+d V(x) ub = const. t d x

  6. Use production cost for pricing: t = c(x) + d nonlinear pricing t = t + c´(x)(x - x) linear pricing

  7. 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

  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

  10. 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

  11. Determining price levels q0 first: t0=V(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

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