Let's examine the original Payoff Matrix again. If the Prisoners could somehow agree to both Deny an knowledge of the crime they would each spend 6 months in jail then the charges would be dropped. By playing their dominant strategy of Confessing they both are convicted of felonies and serve a total of 3 years. Why don't they cooperate?

It might seem at first that the reason they don't cooperate is that they aren't allowed to discuss strategy with one another. Suppose they are. What could Prisoner 1 say to Prisoner 2 to induce her to Deny?

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