Game Theory Lab: Payoffs and Best Responses
Edit a two-player payoff matrix to find best responses, strict dominance, and pure-strategy Nash equilibria.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 10 minutes.
How does it work?
- Change the controls or open a named preset. Read the outputs, then check a challenge.
What will you get?
Compare the model’s outputs and check two challenges.
What does the model assume?
- Two players choose simultaneously between two strategies each. A payoff pair lists Row’s payoff first and Column’s second.
- Larger payoffs are preferred. Numbers are illustrative utility values, not money or a forecast.
- A best response includes tied maximizers. Strict dominance requires a strictly higher payoff against each opposing strategy.
- A pure-strategy equilibrium permits no profitable unilateral change. This model does not calculate mixed-strategy equilibria.
- An equilibrium is marked as improvable when another cell gives both players strictly higher payoffs; this is a comparison of outcomes, not a predicted agreement.
Which setup would you like to try?
What can you change?
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
Range: -10 to 10 utility.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Row’s best response to Left | Down | |
| Row’s best response to Right | Down | |
| Column’s best response to Up | Right | |
| Column’s best response to Down | Right | |
| Row’s strictly dominant strategy | Down | |
| Column’s strictly dominant strategy | Right | |
| Pure-strategy Nash equilibria | Down, Right | |
| Equilibria with an outcome better for both | Down, Right |
Payoffs are Row, Column. A star marks a best response to the other player’s choice; two stars identify an equilibrium. A dashed outline marks an equilibrium cell.
Can you reach these targets?
Keep the other prisoner’s-dilemma payoffs shown below. Change the two Up-Left payoffs so Up and Left become strict best responses to one another.
- Target: Row payoff at Up, Right = 0 utility; tolerance 0 utility.
- Target: Column payoff at Up, Right = 5 utility; tolerance 0 utility.
- Target: Row payoff at Down, Left = 5 utility; tolerance 0 utility.
- Target: Column payoff at Down, Left = 0 utility; tolerance 0 utility.
- Target: Row payoff at Down, Right = 1 utility; tolerance 0 utility.
- Target: Column payoff at Down, Right = 1 utility; tolerance 0 utility.
- Row’s best response to Left (Up)
- Column’s best response to Up (Left)
Reproduce the displayed matching-payoff game with no pure-strategy equilibrium.
- Target: Row payoff at Up, Left = 1 utility; tolerance 0 utility.
- Target: Column payoff at Up, Left = -1 utility; tolerance 0 utility.
- Target: Row payoff at Up, Right = -1 utility; tolerance 0 utility.
- Target: Column payoff at Up, Right = 1 utility; tolerance 0 utility.
- Target: Row payoff at Down, Left = -1 utility; tolerance 0 utility.
- Target: Column payoff at Down, Left = 1 utility; tolerance 0 utility.
- Target: Row payoff at Down, Right = 1 utility; tolerance 0 utility.
- Target: Column payoff at Down, Right = -1 utility; tolerance 0 utility.
- Pure-strategy Nash equilibria (No pure-strategy equilibrium)