Why does cooperation emerge among selfish individuals who only seek their own benefit? This upper-secondary lab rebuilds Robert Axelrod's famous experiment (1980): a tournament where different strategies face each other playing the prisoner's dilemma over and over. From the one-shot dilemma we move to the repeated game, to the everyone-vs-everyone tournament and, finally, to evolutionary models —including spatial ones— that show how cooperation can emerge… or collapse. The conclusion is surprising: the winning strategy is not the cleverest or the most aggressive, but a very simple one based on reciprocity.

What you learn

The core idea: in a world of repeated interactions, cooperating can be rational, and cooperation can emerge and sustain itself even without prior trust or an authority to impose it — but it can also collapse easily.

• Understand the dilemma (rooms 1-8). The payoff matrix (reward, temptation, punishment, sucker), the Nash equilibrium, real examples (the Cold War, teamwork, three classmates who copy each other), the one-shot dilemma and its trap, and why the repeated game with an uncertain ending —the shadow of the future— changes the rules.
• The strategies (rooms 9-11). The classics of the tournament (Tit-for-Tat, Cooperator, Defector, Random, Grudger, Pavlov), Axelrod's surprising result (the nice ones win; the Defector sinks) and how everything changes with the composition: in a class of defectors, cooperating no longer pays.
• Build your strategy (room 12). A builder: a first move + a loop of rules (including a fine 2×2 table of defection probability by the rival's last two moves). It is tested in real-time matches and taken to the class tournament.
• Tournament and evolution (rooms 13-14). The class tournament (the teacher collects the students' strategies and adds famous ones) and the evolutionary tournament: replicator dynamics, where the best scorers reproduce generation by generation.
• Social consequences (rooms 15-16). Two spatial models: a cellular automaton where lone cooperators die but survive and spread in clusters (spatial reciprocity), and the defection gene, where a tiny selfish mutation is enough for cooperation to collapse (the tragedy of the commons, emerging on its own).

Key mathematical ideas

• Prisoner's dilemma: T > R > P > S and 2R > T + S. Defecting is the one-shot dominant strategy, yet it leads to a worse outcome for both than cooperating.
• Nash equilibrium vs Pareto optimum: the stable point (Defect, Defect) does not match the best for the pair (Cooperate, Cooperate). The tragedy of the commons in miniature.
• Repeated game and the shadow of the future: with an uncertain number of rounds there is no backward induction, and reciprocity (Tit-for-Tat) becomes viable.
• Direct reciprocity: cooperating conditional on the other cooperating; why such a simple rule as Tit-for-Tat survives a whole tournament without winning a single duel.
• Evolutionary (replicator) dynamics: each strategy's frequency grows in proportion to its payoff advantage; it allows the study of invasion, coexistence and dominance depending on the initial mix.
• Spatial reciprocity (Nowak & May, 1992): on a grid, cooperators survive and spread by forming clusters even though they would lose in a well-mixed population — spatial structure changes the result.
• Mutation–selection and the tragedy of the commons: starting from pure cooperation, a small "selfish" mutation is selected and spreads; with no structure to stop it, cooperation erodes until it collapses.