Game Theory Payoff Calculator
Analyze strategic decisions using payoff matrices and find Nash Equilibria.
Why Game Theory Matters
Game Theory analyzes strategic interactions where the outcome for each participant depends on the choices of others. It's used in economics, business, politics, biology, and AI to model competition, cooperation, and negotiation.
How to Use This Calculator
Enter the payoffs for two players in a 2×2 decision matrix (e.g., Cooperate/Defect). The calculator evaluates each outcome to find Nash Equilibria — stable strategy pairs where neither player benefits from changing their move alone.
The Nash Equilibrium Concept
A strategy profile is a Nash Equilibrium if no player can gain by changing their strategy while others keep theirs fixed.This helps predict stable outcomes in competitive scenarios, even when cooperation would yield better collective results (like in the Prisoner’s Dilemma).
Example Games
- Prisoner’s Dilemma: Both defecting is the equilibrium, even though mutual cooperation is better.
- Chicken: Two equilibria exist — one where each player swerves.
- Coordination Game: Multiple equilibria where both players choose the same action.
Real-World Applications
- Pricing Wars: Predict competitor pricing strategies
- Negotiations: Find stable bargaining outcomes
- Auctions: Model bidder behavior
- AI & Robotics: Multi-agent decision systems
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