CE-Solver v0.1, Sep 2008, Martin Hruby, FIT BUT, hrubym@fit.vutbr.cz Loading a game of 8 players with: 9 1 10 10 10 1 10 3 strategies Game loaded CorrSolver: creating profiles ====================================================================== 270000 LP-variables empty/non-empty 0/270000 profiles ====================================================================== Generating player 0, 9 strategies Generating player 2, 10 strategies Generating player 3, 10 strategies Generating player 4, 10 strategies G-matrix 4 0 9: Generating player 5, 1 strategies Generating player 6, 10 strategies Generating player 1, 1 strategies Generating player 7, 3 strategies G-matrix 0 0 8: G-matrix 2 0 9: G-matrix 6 0 9: G-matrix 7 0 2: G-matrix 3 0 9: | 0 27000 [0] G-matrix 2 0 8: | 0 0 [0] G-matrix 2 0 7: | 0 0 [0] G-matrix 2 0 6: | 0 0 [0] G-matrix 2 0 5: | 0 0 [0] G-matrix 2 0 4: | 0 27000 [0] G-matrix 6 0 8: | 0 0 [0] G-matrix 2 0 3: | 0 0 [0] G-matrix 6 0 7: | 0 0 [0] G-matrix 2 0 2: | 0 0 [0] G-matrix 6 0 6: | 0 0 [0] G-matrix 2 0 1: | 0 0 [0] G-matrix 6 0 5: | 0 0 [0] G-matrix 2 1 9: | 0 0 [0] G-matrix 6 0 4: | 0 0 [0] G-matrix 6 0 3: | 0 0 [0] G-matrix 6 0 2: | 0 25992 [0] G-matrix 3 0 8: | 0 0 [0] G-matrix 6 0 1: | 0 0 [0] G-matrix 3 0 7: | 0 0 [0] G-matrix 6 1 9: | 0 0 [0] G-matrix 3 0 6: | 0 0 [0] G-matrix 3 0 5: | 0 0 [0] G-matrix 3 0 4: | 0 0 [0] G-matrix 3 0 3: | 0 0 [0] G-matrix 3 0 2: | 0 0 [0] G-matrix 3 0 1: | 0 0 [0] G-matrix 3 1 9: | 0 24318 [0] G-matrix 4 0 8: | 0 0 [0] G-matrix 4 0 7: | 28131 0 [0] G-matrix 0 0 7: | 0 0 [28131] G-matrix 4 0 6: | 0 0 [28131] G-matrix 4 0 5: | 0 0 [28131] G-matrix 4 0 4: | 0 0 [28131] G-matrix 4 0 3: | 0 21816 [28131] G-matrix 2 1 8: | 0 0 [28131] G-matrix 4 0 2: | 0 0 [28131] G-matrix 2 1 7: | 0 0 [28131] G-matrix 4 0 1: | 0 0 [28131] G-matrix 2 1 6: | 0 0 [28131] G-matrix 4 1 9: | 0 0 [28131] G-matrix 2 1 5: | 0 0 [28131] G-matrix 2 1 4: | 0 0 [28131] G-matrix 2 1 3: | 0 0 [28131] G-matrix 2 1 2: | 0 0 [28131] G-matrix 2 1 0: | 0 0 [28131] G-matrix 2 2 9: | 0 19899 [28131] G-matrix 6 1 8: | 0 0 [28131] G-matrix 6 1 7: | 0 0 [28131] G-matrix 6 1 6: | 0 0 [28131] G-matrix 6 1 5: | 0 0 [28131] G-matrix 6 1 4: | 0 0 [28131] G-matrix 6 1 3: | 0 0 [28131] G-matrix 6 1 2: | 0 0 [28131] G-matrix 6 1 0: | 0 0 [28131] G-matrix 6 2 9: | 0 16468 [28131] G-matrix 4 1 8: | 0 0 [28131] G-matrix 4 1 7: | 0 0 [28131] G-matrix 4 1 6: | 0 0 [28131] G-matrix 4 1 5: | 0 0 [28131] G-matrix 4 5 7: G-matrix 3 5 9: | 0 0 [58033] G-matrix 2 5 7: | 0 0 [58033] G-matrix 4 5 6: | 0 0 [58033] G-matrix 2 5 6: | 0 0 [58033] G-matrix 4 5 4: | 0 444 [58033] G-matrix 0 1 7: | 4996 0 [58033] G-matrix 7 2 0: | 0 0 [63029] G-matrix 2 5 4: | 0 0 [63029] G-matrix 4 5 3: | 0 0 [63029] G-matrix 0 1 6: | 0 0 [63029] G-matrix 4 5 2: | 0 0 [63029] G-matrix 2 5 3: | 0 0 [63029] G-matrix 4 5 1: | 0 0 [63029] G-matrix 0 1 5: | 0 0 [63029] G-matrix 2 5 2: | 0 0 [63029] G-matrix 4 5 0: | 2560 0 [63029] | 0 0 [65589] G-matrix 0 1 4: | 0 0 [65589] G-matrix 4 6 9: | 0 576 [65589] G-matrix 3 5 8: | 0 0 [65589] G-matrix 2 5 1: | 0 0 [65589] G-matrix 3 5 7: | 0 512 [65589] G-matrix 4 6 8: | 0 0 [65589] G-matrix 0 1 3: | 0 0 [65589] G-matrix 2 5 0: | 0 0 [65589] | 0 0 [65589] G-matrix 3 5 6: G-matrix 4 6 7: | 0 0 [65589] G-matrix 0 1 2: | 0 0 [65589] | 0 0 [65589] G-matrix 4 6 5: G-matrix 3 5 4: | 0 0 [65589] G-matrix 2 6 9: | 0 0 [65589] G-matrix 0 1 0: | 0 0 [65589] | 0 0 [65589] G-matrix 3 5 3: G-matrix 4 6 4: | 0 0 [65589] G-matrix 0 2 8: | 0 384 [65589] G-matrix 2 6 8: | 0 0 [65589] G-matrix 4 6 3: | 0 0 [65589] G-matrix 3 5 2: | 144 0 [65589] G-matrix 6 6 4: G-matrix 2 7 5: | 0 0 [66508] G-matrix 4 7 5: | 0 96 [66508] G-matrix 3 7 8: | 0 0 [66508] | 0 0 [66508] G-matrix 6 6 3: G-matrix 2 7 4: | 0 0 [66508] | 0 0 [66508] G-matrix 4 7 4: G-matrix 3 7 6: | 0 0 [66508] | 0 0 [66508] G-matrix 2 7 3: G-matrix 6 6 2: | 0 0 [66508] | 0 0 [66508] G-matrix 3 7 5: G-matrix 4 7 3: | 0 0 [66508] | 0 0 [66508] G-matrix 2 7 2: G-matrix 6 6 1: | 0 0 [66508] | 0 0 [66508] G-matrix 3 7 4: G-matrix 4 7 2: | 0 0 [66508] G-matrix 6 6 0: | 0 0 [66508] | 0 0 [66508] G-matrix 4 7 1: G-matrix 3 7 3: | 0 90 [66508] G-matrix 0 3 8: | 0 0 [66508] G-matrix 6 7 9: | 0 0 [66508] | 0 0 [66508] G-matrix 3 7 2: G-matrix 2 7 1: | 0 24 [66508] G-matrix 0 3 7: | 0 0 [66508] | 0 0 [66508] G-matrix 2 7 0: G-matrix 4 7 0: | 0 56 [66508] G-matrix 6 7 8: | 0 0 [66508] | 0 0 [66508] G-matrix 4 8 9: G-matrix 2 8 9: | 0 0 [66508] G-matrix 3 7 1: | 0 0 [66508] G-matrix 0 3 6: | 0 0 [66508] G-matrix 6 7 6: | 0 0 [66508] G-matrix 3 7 0: | 0 48 [66508] G-matrix 4 8 7: | 0 0 [66508] G-matrix 0 3 5: | 0 0 [66508] | 0 0 [66508] G-matrix 4 8 6: G-matrix 3 8 9: | 0 0 [66508] G-matrix 6 7 5: | 0 0 [66508] Reduced game: Player-0 has the resulting strategies: 0 Player-1 has the resulting strategies: 0 Player-2 has the resulting strategies: 9 Player-3 has the resulting strategies: 9 Player-4 has the resulting strategies: 9 Player-5 has the resulting strategies: 0 Player-6 has the resulting strategies: 9 Player-7 has the resulting strategies: 2 lps.work; 47 constraints, 1 lp-variables 46 non-zero matrix elements 0: objval = 0.000000000e+00 infeas = 1.000000000e+00 (0) 1: objval = 5.596271411e+10 infeas = 0.000000000e+00 (1) OPTIMAL SOLUTION FOUND CE-Probability distribution Lp-Variable(profile number): 1 1.00 0 0 9 9 9 0 9 2 52610260992 -5835 992797184 556932160 1150354176 -5835 157363072 495018304 Solution-profile: 29999 1 items in the stochastic profile profile num: 29999 [ 0 0 9 9 9 0 9 2 ] 1.00

The CE-Solver results with a profile "[ 0 0 9 9 9 0 9 2 ]" where the players have outcomes "52610260992 -5835 992797184 556932160 1150354176 -5835 157363072 495018304". Probability of this profile is 1.00. If the resulting equilibrium is not in pure strategies, the program will display the computed mixed equilibrium (probability distribution on profiles).

We may see that in this particular example the 8-player game was reduced to a single profile, so all players have a strategy which strictly dominates the others.