Finally, to see that no player has an incentive to deviate from s, fix any history h on the equilibrium path. If Player i deviates at h, she obtains maxa EA, ui(ai, s_(h))+5v exists 82 such that 8>8 implies that the deviation is not profitable at h. And, since/, o because her opponents will minmax her, and she will best-respond to p_i4 Clearly, ther on the equilibrium path, it follows that the deviation is not profitable ex-ante Thus, for 8>8=max(8,8), w(8)is the Nash equilibrium payoff profile, and J(8 u|<e, as required.■ You can see that the specification of the strategies is rather awkward. Machines greatly simplify the task, as I will ask you to verify in the next problem set ANote the role of the equilibrium assumption: in principle, Player i could hope that a lower-indexed player j also deviates at h, but in equilibrium this does not happen. Hence, she expects to be the only deviator atFinally, to see that no player has an incentive to deviate from s, fix any history h on the equilibrium path. If Player i deviates at h, she obtains maxai∈Ai ui(ai , s−i(h)) + δ 1−δ vi , because her opponents will minmax her, and she will best-respond to p−i . 4 Clearly, there exists δ 2 such that δ > δ2 implies that the deviation is not profitable at h. And, since h is on the equilibrium path, it follows that the deviation is not profitable ex-ante. Thus, for δ > δ = max(δ 1 , δ2 ), w 0 (δ) is the Nash equilibrium payoff profile, and |w 0 (δ) − w| < , as required. You can see that the specification of the strategies is rather awkward. Machines greatly simplify the task, as I will ask you to verify in the next problem set. 4Note the role of the equilibrium assumption: in principle, Player i could hope that a lower-indexed player j also deviates at h, but in equilibrium this does not happen. Hence, she expects to be the only deviator at h. 6