Table 1

Conditional probability that a PNE is not PPO in an n-player game where each player has m actions

Actions per player mNumbers of players n
23456
2S 0.1098S 0.1257S 0.1080S 0.0814S 0.0544
I 0.1111I 0.1211
F 0.1111F 0.1241F 0.1051F 0.0803F 0.0582
3S 0.1911S 0.2057S 0.1688S 0.1102*
I 0.1992I 0.1976
F 0.1992F 0.2021F 0.1662
4S 0.2376S 0.2531S 0.1951
I 0.2492I 0.2341
F 0.2492F 0.2401
5S 0.2760S 0.2654S 0.2168
I 0.2802I 0.2541
F 0.2802
6S 0.3063S 0.2837S 0.2352
I 0.3010
F 0.3010
  • S, based on 2,500 simulations; I, based on numerical integration of Eq. 2, F, based on summation of the finite series 6

  • * Only 500 simulations.