Brain Teasers · The Split Deal
Prisoner's Dilemma Puzzle - Why Both Testify
The prisoner's dilemma played as a story: two thieves, separate rooms, and one offer each.
What is the prisoner's dilemma?
The prisoner's dilemma is the best-known model in game theory for the conflict between individual and collective rationality. Two players each choose, without communicating, whether to cooperate or defect. Mutual cooperation gives both a good outcome; mutual defection gives both a worse outcome; but if one cooperates while the other defects, the defector does best of all and the cooperator does worst. The game was devised in 1950 by Merrill Flood and Melvin Dresher at RAND Corporation, and the prison-sentence framing that gave it its name and its lasting popularity came shortly after from the mathematician Albert Tucker.
The defining feature is that defection is a dominant strategy: whatever the other player does, you are individually better off defecting. Since the game is symmetric, both players reason their way to defection, and mutual defection is the unique Nash equilibrium - a state where neither player can improve their own outcome by switching alone. The paradox is that this equilibrium is worse for both players than the mutual-cooperation outcome they both walked away from, purely because neither could risk being the one who cooperates while the other defects.
This gap between what is individually rational and what is collectively best is what makes the prisoner's dilemma useful far outside its prison-cell story. It is the standard model for arms races, price wars between competing firms, overfishing of a shared resource, and failures to cooperate on collective problems like emissions - any situation where each party has a private incentive to defect from an arrangement that would leave everyone better off if it held.
A large body of later work studies what happens when the game is repeated - the 'iterated prisoner's dilemma' - because repetition opens the door to strategies like tit-for-tat that can sustain cooperation by threatening future retaliation for defection, something the single-shot game's logic can never support.
How it works
Ada and Bo are held in separate rooms and each offered the same deal: testify and your own sentence is wiped. Silent together they serve 1 year each; both testifying costs 8 each; one testifying while the other stays silent frees the talker and costs the silent one 10. The story shows the full payoff matrix, then asks what each one does. You type a guess, lock it in, and step through the answer and breakdown.
How scoring works
There is no grading - your typed guess is shown back beside the real answer. The story teasers share a single lifetime unlock for free users, so one reveal locks the group.
The key insight
Fix the other player's choice and compare your own options against it. Whatever Bo does, Ada is better off testifying - a dominant strategy - and the game is symmetric, so both testify and serve 8 years even though mutual silence costs 1 each. The equilibrium is stable because neither can improve alone, and it is still worse for both than the outcome they rejected.
The full step-by-step solution lives at /brain-teasers/prisoners-dilemma/solution.
A worked example
Suppose Bo stays silent: Ada gets 1 year silent, 0 testifying - testify wins. Suppose Bo testifies: Ada gets 10 silent, 8 testifying - testify wins again. One option won both cases, so Ada never needs to guess Bo's move, and Bo runs the identical reasoning.
Common mistakes
• Answering 'both stay silent because it is best overall' - jointly best and individually stable are different properties.
• Trying to reason about both players' moves at once instead of fixing one and comparing.
• Calling mutual silence an equilibrium - either player gains by defecting from it.
Why interviews test this
Interviewers use this to check you can find a dominant strategy case by case and attach the terms 'dominant strategy' and 'Nash equilibrium' to the right cells. The written solution at /brain-teasers/prisoners-dilemma/solution covers what breaks the trap.
Play The Split Deal on Outcry
The Split Deal is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play The Split Deal and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.