If Tim tells the truth with probability $p$, you simply get that you should guess what he said if $p<\frac{1}{1000000}$, and $p>\frac{1}{1000000}$. For Tim the optimal choice is to have $p=\frac{1}{1000000}$ in order not to give you any information: Anything else is playing on psychology and human biases, which exist in reality but trying to play a “perfect” game by assuming your opponent is not also leaves you vulnerable to exploitability, as you mentioned.
It seems you are trying to get a deeper understanding of human fallibility rather than playing optimal games. Have I misunderstood it?
If Tim tells the truth with probability $p$, you simply get that you should guess what he said if $p<\frac{1}{1000000}$, and $p>\frac{1}{1000000}$. For Tim the optimal choice is to have $p=\frac{1}{1000000}$ in order not to give you any information: Anything else is playing on psychology and human biases, which exist in reality but trying to play a “perfect” game by assuming your opponent is not also leaves you vulnerable to exploitability, as you mentioned.
It seems you are trying to get a deeper understanding of human fallibility rather than playing optimal games. Have I misunderstood it?
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