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If Prisoner 1 believes that Prisoner 2 will Deny it can either Confess and be released immediately (payoff of 0) or it can Deny and face jail for 6 months (payoff of - 1/2).
It is better for Prisoner 1 to Confess since freedom is better than 6 months in jail. In fact, Prisoner 1 should always Confess no matter what Prisoner 2 does, Confess is a dominant strategy
At this point some students begin to wonder about guilt, loyalty and similar feelings which may motivate different behavior. If these are important to Prisoner 1 in this case we would need to construct a payoff matrix which accounted for these too. Here we are anaylizing the game when both players care only about time spent in custody.
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