Skip to main content
Calcimator

Game Theory Payoff Calculator

Analyze a 2x2 payoff matrix to find dominant strategies, Nash equilibria (pure and mixed), minimax values, and Pareto optimality.

Inputs

Results

P1 Dominant (0=None,1=Up,2=Down)

2

P2 Dominant (0=None,1=Left,2=Right)

2

Pure Nash Equilibria1
Nash P1 Payoff1
Nash P2 Payoff1
Mixed Strategy P1 (prob Up)-1
Mixed Strategy P2 (prob Left)-1
Minimax Value P11
Minimax Value P21
Pareto Optimal Outcomes3
How to Use This Calculator
  1. Enter the payoff matrix values for Player 1 and Player 2 for each of the four strategy combinations (Up-Left, Up-Right, Down-Left, Down-Right).
  2. Review the dominant strategies for each player if they exist.
  3. Check for pure-strategy Nash equilibria, where neither player benefits from unilaterally changing strategy, along with the payoffs at that equilibrium.
  4. Review the mixed-strategy Nash equilibrium probabilities for each player.
  5. Use the minimax values and Pareto optimal outcome count to guide strategy selection in adversarial scenarios.

What each input means

P1 Payoff: Up-Left
Player 1's payoff when P1 plays Up and P2 plays Left
P1 Payoff: Up-Right
Player 1's payoff when P1 plays Up and P2 plays Right
P1 Payoff: Down-Left
Player 1's payoff when P1 plays Down and P2 plays Left
P1 Payoff: Down-Right
Player 1's payoff when P1 plays Down and P2 plays Right
P2 Payoff: Up-Left
Player 2's payoff when P1 plays Up and P2 plays Left
P2 Payoff: Up-Right
Player 2's payoff when P1 plays Up and P2 plays Right
P2 Payoff: Down-Left
Player 2's payoff when P1 plays Down and P2 plays Left
P2 Payoff: Down-Right
Player 2's payoff when P1 plays Down and P2 plays Right

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    P1 Payoff: Up-Left = 3, P1 Payoff: Up-Right = 0, P1 Payoff: Down-Left = 5, P1 Payoff: Down-Right = 1 = 8 input(s) provided
  2. Calculate P1 Dominant
    P1 Dominant
    2 = 2
  3. Calculate P2 Dominant
    P2 Dominant
    2 = 2
  4. Calculate Pure Nash Equilibria
    Pure Nash Equilibria
    1 = 1
  5. Calculate Nash P1 Payoff
    Nash P1 Payoff
    1 = 1

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Logic & Formal Reasoning

Decision Matrix Calculator

Compare two options using weighted scoring across 4 criteria. Calculates normalized totals, winner, and sensitivity analysis.

Logic & Formal Reasoning

Probability Tree Calculator

Calculate sequential and combined probabilities for multi-stage probability trees with up to 4 branches.

Logic & Formal Reasoning

Boolean Algebra Simplifier

Estimate Boolean expression simplification from sum-of-products form. Calculates term and literal reduction using grouping heuristics.

More in Math & Statistics.