Time exception and optimal value
There are Attacker and Defencer in a computer server,
Defencer start from S0 to defend the server, he will upgrade the defence system after each T0 start from S0.
Attacker start from S1 to attack the server, he will upgrade the attack program after each T1 start from S1.
After an upgrade of the attacker or defencer, the attacker/defencer will get the control of the server.
The value of T0 and T1 is known, Defencer know T1 but don't know S1.
a.) Find the time exception of the system which is controlled by Defencer.
b.) For every p second, the defender will get 1 coin if he is controlling the server. But he need to cost K coin to upgrade the defence system.
T1 > 2K, Find the optimal value of T0.