1. S ystems Analysis Laboratory Helsinki University of Technology 1 Harri Ehtamo Kimmo Berg Mitri Kitti On Tariff Adjustment in a Principal Agent Game Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi

2. S ystems Analysis Laboratory Helsinki University of Technology 2 Principal-agent games Seller-buyer price tariff Manager-worker wage contract Taxation Public good (Groves mechanism, 1973) Auctions Bargaining

3. S ystems Analysis Laboratory Helsinki University of Technology 3 A seller-buyer game u s (t, x)=t – c(x) u b (t, x)=V(x) - t max u b (t(x), x)(IC) V(x) - t(x) = 0(IR) x0x0

4. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 5 The linear tariff: u b = const. c(x)+  x t V(x) u s = const. 

6. S ystems Analysis Laboratory Helsinki University of Technology 6 Use production cost for pricing: t = c(x) +  nonlinear pricing t = t + c´(x)(x - x)linear pricing

7. S ystems Analysis Laboratory Helsinki University of Technology 7 Incomplete information –high and low consumer  H V(x),  L V(x); V(x) known; p H, p L known Compute BN-equilibrium directly, or use revelation principle Here: V H, V L unknown => use adjustment processes

8. S ystems Analysis Laboratory Helsinki University of Technology 8 BR-dynamics q1q1 q2q2 q 1 = r 1 (q 2 ) q 2 = r 2 (q 1 ) q10q10 q12q12 q21q21

9. S ystems Analysis Laboratory Helsinki University of Technology 9 “BR”-adjustment of the linear contract t = t + c´(x)(x - x) x t...

10. S ystems Analysis Laboratory Helsinki University of Technology 10 Bayesian Nash equilibrium Highest type first: V´(  H,x H ) = c´(x H ) Other types in descending order: Find x i F[V´(  i,x i ),V´(  i+1,x i ),c´(x i )]=0i = 0,...,H-1

11. S ystems Analysis Laboratory Helsinki University of Technology 11 Determining price levels quantities known  0 first: t 0 =V(  0,x 0 ) Other types: Indifferent to the previous bundle t0t0 x0x0 xixi titi

12. S ystems Analysis Laboratory Helsinki University of Technology 12 Optimal bundles by adjustment type Highest Lowest quantities prices Start End Simple Adjustment rules with approximations