Play simultaneous-move games against a simulated opponent — explore Nash equilibria, dominant strategies & cooperation
| Opp: Cooperate | Opp: Defect | |
|---|---|---|
| You: Cooperate | 3, 3 | 0, 5 |
| You: Defect | 5, 0 | 1, 1 |
This lab lets you explore the structure of \(2 \times 2\) simultaneous-move games. Each cell in the payoff matrix shows \((\text{your payoff}, \text{opponent's payoff})\). In a symmetric game the opponent's payoffs mirror yours: when you cooperate and they defect, you receive the "sucker's" payoff \(S\) while they receive the "temptation" \(T\), and vice versa. The four payoff parameters — \(R\) (reward for mutual cooperation), \(T\) (temptation to defect), \(S\) (sucker's payoff), and \(P\) (punishment for mutual defection) — fully determine the game's strategic structure.
The best-response chart shows how your expected payoff from each action varies with the probability \(q\) that your opponent cooperates. Where the cooperate line lies above the defect line, cooperation is your best response; where it lies below, defection is. If the lines cross in the interior, the intersection gives the mixed-strategy Nash equilibrium — the probability at which you are exactly indifferent between your two actions: \(q^* = (P - S)/(R - T + P - S)\). The famous games differ precisely in the ordering of \(R, T, S, P\): the Prisoner's Dilemma has \(T > R > P > S\), making defection dominant despite mutual cooperation being Pareto superior.
By playing repeated rounds against different AI strategies, you can experience how the shadow of the future transforms one-shot incentives. Tit-for-Tat, for instance, sustains cooperation in the iterated Prisoner's Dilemma by making defection costly — your opponent retaliates next round. Try switching between game presets and opponent strategies to see how the equilibrium structure and cooperative possibilities change across different strategic environments.