Short label for choice A (e.g., A, Opera, Cooperate)
Short label for choice B (e.g., B, Football, Defect)
2x2 Matrix Games
How It Works
Two players simultaneously choose action A or B. The payoff each player receives depends on both players' choices, as shown in the payoff matrix.
Each cell shows (P1 payoff, P2 payoff). The highlighted cell shows the outcome of the current round.
Game Types
Game
Description
Battle of the Sexes
Coordination game - both prefer to match, but disagree on which outcome is best
Prisoner's Dilemma
Classic dilemma - mutual cooperation (A,A) is better than mutual defection (B,B), but defecting is individually rational
Second Best
Players' first choices differ, creating tension between individual and collective optimality
Unfair / Biased
Asymmetric games where one player has an inherent advantage
Matching Pennies
Zero-sum game with no pure Nash equilibrium - P1 wins if actions match, P2 wins if they differ
Win-Win
Coordination game where players can achieve mutual benefit
Custom
Edit payoff values directly to create any 2x2 game
Nash Equilibrium
A Nash equilibrium is an outcome where neither player can improve by unilaterally changing their choice. Some games have one equilibrium, some have multiple, and some have none in pure strategies.
Tips
Watch how LLMs reason about strategic situations in the right panel. Do they find the Nash equilibrium? Do they attempt cooperation? How do they adapt over multiple rounds?