NASH EQUILIBRIUM / MATHEMATICAL GUIDE
Nash Equilibrium Guide
Read payoff matrices and identify best responses and equilibria.
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Models and worked examples
01 / NASH
Prisoner’s Dilemma
Example payoff matrix: C/C (3,3) · C/D (0,5) · D/C (5,0) · D/D (1,1)
Equilibrium: (D,D)
02 / NASH
Coordination Game
Example payoff matrix: A/A (4,4) · A/B (0,0) · B/A (0,0) · B/B (2,2)
Equilibrium: (A,A), (B,B)
03 / NASH
Matching Pennies
Example payoff matrix: A/A (1,−1) · A/B (−1,1) · B/A (−1,1) · B/B (1,−1)
Equilibrium: No pure Nash; each mixes A and B 50/50
How to find an equilibrium
Identify each player’s highest-payoff response to every fixed opponent strategy. A cell is a pure-strategy Nash equilibrium if both players are best-responding there. For mixed strategies, solve the relevant indifference conditions and verify probabilities.
This page provides worked examples, not a live calculator. The computational tool has not yet been activated.
Evidence and source policy
A DOI identifies a research object; it does not by itself prove independent peer review or validation. Journal articles, preprints, manuscripts and proposed models must be labelled separately.
Editor and website developer: Anastasia IVANOVA · GAME THEORY ATLAS / 2026