Nash Equilibrium Calculator

Calculate Nash equilibria, dominant strategies, and analyze payoff matrices. Essential tool for economics, political science, and decision analysis.

Normal Form
Zero-Sum Game
Repeated Game
Evolutionary Game
Multi-Player (3+)
2×2
2×3
3×2
3×3
Custom
Payoff Matrix

Player 1's payoff is shown first, Player 2's payoff second (P1, P2)

Prisoner's Dilemma
Chicken Game
Stag Hunt
Matching Pennies
Battle of the Sexes
Coordination
Hawk-Dove
Public Goods
Ultimatum Game
Analyzing game...

Advanced Game Theory Analysis

Multi-Player Game Analysis

Multi-player games introduce new equilibrium concepts and strategic considerations:

  • k-equilibria: Coalitions of k players can deviate together
  • Strong Nash Equilibrium: No coalition of any size can deviate profitably
  • Coalition-proof Nash Equilibrium: Self-enforcing agreements within coalitions
  • Network Effects: Players' payoffs depend on others' choices
Repeated Game Theory

When games are repeated, cooperation can emerge through strategies like:

  • Grim Trigger: Permanent punishment after any defection
  • Tit-for-Tat: Mimic opponent's previous move
  • Forgiving Strategies: Occasional cooperation even after defection
  • Folk Theorems: Many equilibria are possible with sufficiently patient players

Discount Factor (δ): Future payoffs are discounted by δ per period. Higher δ makes future cooperation more valuable.

Evolutionary Game Theory

Evolutionary dynamics describe how strategies spread in populations:

  • Replicator Dynamics: Strategies grow at rate proportional to their relative payoff
  • Evolutionary Stable Strategy (ESS): Strategy that cannot be invaded by mutants
  • Adaptive Dynamics: Continuous strategy evolution
  • Cultural Evolution: Strategy transmission through imitation and learning

User Q&A

This calculator is designed to help students, researchers, and professionals analyze strategic interactions in various game theory scenarios. It can find Nash equilibria, identify dominant strategies, analyze repeated and evolutionary games, and provide visualizations to understand complex game dynamics.

The calculator uses standard game theory algorithms to find both pure and mixed strategy Nash equilibria. For 2×2 games, it calculates exact mixed strategy probabilities. For larger games, it finds all pure strategy equilibria. The algorithms have been tested against known game theory examples and produce correct results.

Yes! The calculator supports multi-player games with 3 to 5 players. Select the "Multi-Player (3+)" game type and configure each player's strategies. The calculator uses different representations (3D tensor for 3 players, multiple 2D matrices, or simplified symmetric form) to analyze these complex interactions.

Repeated games involve the same players interacting multiple times, allowing for strategies like Tit-for-Tat or Grim Trigger. Evolutionary games model how strategies spread in a population over generations through processes like imitation and selection. The calculator can simulate both types with configurable parameters.

In a mixed strategy Nash equilibrium, each player randomizes over their pure strategies with specific probabilities. These probabilities make the opponent indifferent between their own pure strategies. For example, in rock-paper-scissors, the equilibrium is to play each with probability 1/3. The calculator displays these probabilities as percentages in the visualization.

Yes, you can export results in multiple formats:
  • PNG - Screenshot of the complete analysis
  • PDF - Detailed report with matrix data
  • CSV - Raw payoff matrix data for external analysis
The calculator also keeps a history of recent analyses in your browser's local storage.

Many games (like Matching Pennies) don't have pure strategy Nash equilibria. In such cases, the calculator will:
  1. Indicate that no pure strategy Nash equilibria were found
  2. Calculate mixed strategy equilibria for 2×2 games
  3. Suggest considering repeated or evolutionary dynamics
  4. Provide alternative analysis like Pareto efficiency

The example games cover fundamental game theory concepts:
Classical Games:
  • Prisoner's Dilemma - Individual vs collective rationality
  • Battle of the Sexes - Coordination with conflict
  • Chicken Game - Brinkmanship and commitment
Advanced Concepts:
  • Public Goods - Social dilemmas
  • Ultimatum Game - Fairness and bargaining
  • Hawk-Dove - Resource competition
Each example pre-loads a classic payoff matrix, allowing you to instantly see how different concepts play out.