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This page contains Sven and Todd's small collection or equilibrium problems with equilibrium constraints (EPECs). All models are written in AMPL. Each model has several formulations that are distinguished by their filename extensions:

Filename Extension Formulation Type
GJ Gauss-Jacobi formulation
GS Gauss-Seidel formulation
MPEC minimum multiplier formulation; mathematical program with equlilibrium constraints
NCP nonlinear complementarity problem formulation
NCPa alternative NCP formulation (complementarity between multipliers)
NCPt parametric NCP formulation
NLP elastic mode formulation; minimize complementarity
PC price-consistent (square) NCP formulation
PCa alternative price-consistent (square) NCP formulation


  1. 2006-04-27: corrected mistake in outrata4-GS/outrata4-GJ objective definition (now 10*y[4]^2)
  2. 2006-08-23: added data electric-004.dat which is a better conditioned example than electric-003.


A set of problems arising in the modeling of electricity markets.

There are three data files for different networks:

  1. electric-001.dat a small 3 node infeasible problem
  2. electric-002.dat a small 3 node feasible problem
  3. electric-003.dat derived from an 18 node real example of the PJM market from the eastern United States
  4. electric-004.dat a made up example from the PJM example above that is better conditioned.


A set of randomly generated EPECs. The random generator is written in matlab, see epecgen.m *

Sample data files are in three groups (different sizes):

  1. Size 1: 2 leaders with 8 variables and 4 constraints; 16 follower variables
    1. rand-0001.dat
    2. rand-0002.dat
    3. rand-0003.dat
    4. rand-0004.dat
    5. rand-0005.dat
    6. rand-0006.dat
    7. rand-0007.dat
    8. rand-0008.dat
    9. rand-0009.dat
    10. rand-0010.dat
  2. Size 2: 2 leaders with 16 variables and 8 constraints; 32 follower variables
    1. rand-0011.dat
    2. rand-0012.dat
    3. rand-0013.dat
    4. rand-0014.dat
    5. rand-0015.dat
    6. rand-0016.dat
    7. rand-0017.dat
    8. rand-0018.dat
    9. rand-0019.dat
    10. rand-0020.dat
  3. Size 3: 4 leaders with 16 variables and 8 constraints; 32 follower variables
    1. rand-0021.dat
    2. rand-0022.dat
    3. rand-0023.dat
    4. rand-0024.dat
    5. rand-0025.dat
    6. rand-0026.dat
    7. rand-0027.dat
    8. rand-0028.dat
    9. rand-0029.dat
    10. rand-0030.dat


A small EPEC for which with a price-consistent formulations exists:


A small EPEC from Fukushima and Pang which does not have a solution.


An EPEC generated from the outrata3*.mod MPEC models. The control variables from all leaders enter the lower-level problem by averaging over the leaders. This trick ensures that the EPEC does not separate into individual MPECs. This problem has no solution and illustrates the behavior of the solvers when tackling a problem without solution. All Stackelberg players have the same constraints but different objective functions, so the problem has no price-consistent solution.


This EPEC is derived from outrata3 so that a price-consistent solution to this model exists.

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