The whole game hinges on the fact that the players can't communicate and coordinate. But what if they both have the same lawyer? The moment you ask for a lawyer the police can't talk to you without the lawyer present and if its the same lawyer the lawyer can not only communicate with both players as he can indirectly transmit communications between both players. This way the whole game is messed up.
Fatal flaw in the prisoner's dilemma game

Wow, OP is unhinged.
Economists/mathematicians claim that:
if X then Y
OP:
X is not always true
Economists/mathematicians continue to claim that:
if X then YIn addition to this (and yours is actually the main point for what concerns econ for the prisoners example), I'd add that people involved in the same trial, with potentially conflicting interests but relying on the same lawyer, do indeed create a weird situation:
"If attorneys have multiple clients in the same matter, they must disclose the existence of any current or potential conflicts, and where possible and proper, obtain waivers of such conflicts in compliance with the applicable rules of professional responsibility."
https://www.attorneysadvantage.com/RiskManagement/DoYouRepresentMultipleClientsintheSameMatt 
No it doesn't. Have you ever taught the prisoner's dilemma by talking to a student and asking them to agree to the efficient outcome? You then still have an incentive to deviate.
What helps you escape the noncooperative outcome, under the right circumstances, is the existence of repeated games and reputation.

It actually describes reality fairly well. Most people don’t even ask for lawyers, much less attempt to coordinate. And even if they do, as pointed out above, there are ethical restrictions and coordination problems that are inherent in the game anyway.
 I went to law school and multiple friends were prosecutors who ran the game in real life. Just FYI.

If only there was a giant literature based on communication...
Also, you're flat wrong. Even if we can communicate, I still have an incentive to deviate. Communication on it's own doesn't help you escape the noncooperative outcome.This is the right answer. OP gets zero marks on his undergrad micro exam.

The whole game hinges on the fact that the players can't communicate and coordinate. But what if they both have the same lawyer? The moment you ask for a lawyer the police can't talk to you without the lawyer present and if its the same lawyer the lawyer can not only communicate with both players as he can indirectly transmit communications between both players. This way the whole game is messed up.
Attorney client privilege is not protected if the communication tries to cover up a crime. So, your theory is wrong, and the prisoner's dilemma is fine.

There are two distinct issues that are being confused. The first is whether Prisoner's Dilemma accurately models concocted scenarios that correspond to *different* games. Of course, it doesn't.
The second is whether the formal analysis of the formal game corresponding to Prisoner's Dilemma has a "fatal flaw". It doesn't.

No it doesn't.
It kind of does
You're either being obtuse, or don't understand some really basic concepts.
The solution for one twoperson game isn't "kinda" a solution for a different game. No more than saying x = 2 is "kinda" like x = 3. It's a matter of formal mathematics. There's no "kinda" involved.
What you've done come up with a scenario with assumptions that are different from those of Prisoner's Dilemma, that would correspond to a *DIFFERENT* game than Prisoner's Dilemma. Then you argue that there is a "fatal flaw" in Prisoner's Dilemma because it doesn't accurately describe your different game.

No it doesn't.
It kind of does
You're either being obtuse, or don't understand some really basic concepts.
The solution for one twoperson game isn't "kinda" a solution for a different game. No more than saying x = 2 is "kinda" like x = 3. It's a matter of formal mathematics. There's no "kinda" involved.
What you've done come up with a scenario with assumptions that are different from those of Prisoner's Dilemma, that would correspond to a *DIFFERENT* game than Prisoner's Dilemma. Then you argue that there is a "fatal flaw" in Prisoner's Dilemma because it doesn't accurately describe your different game.Of course you are right. But at the same time, if a game does not model reality, what is the point? Is it just for the sake of doing game theory, or should we be trying to explain actual economic behavior? I think the latter is preferred, but much of the game theory literature focuses on the former, which is why it is not used much. Even consultants don't buy it.

No it doesn't.
It kind of does
You're either being obtuse, or don't understand some really basic concepts.
The solution for one twoperson game isn't "kinda" a solution for a different game. No more than saying x = 2 is "kinda" like x = 3. It's a matter of formal mathematics. There's no "kinda" involved.
What you've done come up with a scenario with assumptions that are different from those of Prisoner's Dilemma, that would correspond to a *DIFFERENT* game than Prisoner's Dilemma. Then you argue that there is a "fatal flaw" in Prisoner's Dilemma because it doesn't accurately describe your different game.Hehehe. Calm down. Don't get all stressed out about this. But it kinda does....
OK, in all seriousness, I put this in a test (with an actual game matrix) and the quality of student responses sort of mirror the quality of responses we've seen here today. Obviously what we colloquially call the "prisoners' dilemma" game and what I described were 2 different games and you should now be introducing other things like beliefs into the game.
At least we didn't get a reg y x reply...