What will happen in the second round?
What will happen in the second round? Although some of player 2’s and player 3’s strategies may have been eliminated in the first round, y and z were not, and that ensures that x is not strictly dominated. The same argument ex- plains why y is still not strictly dominated for player 2 in the second round and why z is still not strictly dominated for player 3. Thus, x, y, and z survive two rounds. Like the Energizer Bunny, this argument keeps going and going . . . it works for every round! Thus, if (x, y, z) is a Nash equilibrium, then those strategies survive the IDSDS. Although we have demonstrated this property for a three-player game, the argument is general and applies to all games.