Solution
The Prisoner's Dilemma
Show the problem again
Two suspects are interrogated separately. If both stay silent, each serves 1 year. If one confesses and the other stays silent, the confessor goes free and the other serves 5 years. If both confess, each serves 3 years. In the unique Nash equilibrium, how many years does each suspect serve?
Worked solution
The answer is 3 years each: both confess. Confessing strictly dominates silence: whatever the other player does, confessing reduces your sentence (0 vs 1 if they stay silent, 3 vs 5 if they confess). So both confess in the unique equilibrium, even though mutual silence (1 year each) is better for both, so the equilibrium is not Pareto efficient. Individual rationality and collective optimality diverge.
Source: Devised by Merrill Flood and Melvin Dresher (1950) and given its prisoner framing by Albert Tucker. Statement written for AxiomIQ.