Calculated Strategy Report
This summary appears after submission and stays above the form for quick comparison.
| Outcome | Probability | Payoff A | Payoff B | Weighted A | Weighted B | Pure Nash? |
|---|---|---|---|---|---|---|
| Submit the calculator to generate this table. | ||||||
Calculator Inputs
Enter a payoff matrix, cooperation assumptions, and repeated-game settings. The tool evaluates expectations, dominant actions, pure Nash equilibria, and long-run cooperation thresholds.
Example Data Table
This example uses a classic prisoner dilemma setup where temptation exceeds reward, reward exceeds punishment, and punishment exceeds the sucker payoff.
| Scenario | A action | B action | A payoff | B payoff | Example probability |
|---|---|---|---|---|---|
| Mutual cooperation | Cooperate | Cooperate | 3 | 3 | 24% |
| A exploited | Cooperate | Defect | 0 | 5 | 36% |
| B exploited | Defect | Cooperate | 5 | 0 | 16% |
| Mutual defection | Defect | Defect | 1 | 1 | 24% |
The example probabilities above come from A cooperating 60% of the time and B cooperating 40% of the time.
Formula Used
The calculator applies core game-theory formulas for expected value, best response, pure-strategy equilibrium, and repeated-game sustainability.
1) Outcome probabilities
Pr(CC) = pA × pB
Pr(CD) = pA × (1 - pB)
Pr(DC) = (1 - pA) × pB
Pr(DD) = (1 - pA) × (1 - pB)
2) Expected stage payoff
E[A] = Pr(CC)R + Pr(CD)S + Pr(DC)T + Pr(DD)P
E[B] = Pr(CC)R + Pr(CD)T + Pr(DC)S + Pr(DD)P
3) Best response against an opponent's cooperation chance q
U(Cooperate | q) = qR + (1 - q)S
U(Defect | q) = qT + (1 - q)P
The larger value indicates the best response. Equal values mean the player is indifferent.
4) Discounted repeated value over n rounds
G = (1 - δ^n) / (1 - δ), for δ ≠ 1
Discounted total = Expected stage payoff × G
5) Infinite repeated cooperation threshold with grim trigger
δ* = (T - R) / (T - P)
If the chosen discount factor is at least this threshold, sustained cooperation can be incentive-compatible under a grim-trigger style punishment rule.
How to Use This Calculator
- Enter the four payoffs: temptation, reward, punishment, and sucker payoff.
- Set the estimated cooperation percentages for Prisoner A and Prisoner B.
- Choose a discount factor and number of rounds for repeated-game analysis.
- Press Calculate Strategy to generate the report above the form.
- Review expected payoffs, best responses, pure Nash equilibria, and social efficiency.
- Use Download CSV for a spreadsheet-friendly summary and Download PDF for a portable report.
FAQs
1) What does this calculator measure?
It measures expected payoffs, best responses, pure Nash equilibria, social efficiency, and repeated-game cooperation thresholds from a custom prisoner dilemma payoff matrix.
2) Why are cooperation percentages included?
They convert the payoff matrix into outcome probabilities, allowing the calculator to estimate expected payoffs instead of only listing theoretical outcomes.
3) What makes a matrix a classic prisoner dilemma?
A classic case usually needs temptation greater than reward, reward greater than punishment, punishment greater than the sucker payoff, and mutual cooperation socially preferred.
4) What is a pure Nash equilibrium here?
It is an outcome where neither prisoner can improve their payoff by changing their action alone while the other prisoner's action stays fixed.
5) What does the discount factor mean?
It shows how strongly future payoffs matter. Higher values make long-run cooperation more attractive because future consequences carry more weight.
6) Why can defection still dominate?
In the standard prisoner dilemma, defecting gives a higher payoff whether the other player cooperates or defects, so it becomes the dominant action.
7) What is the social optimum?
It is the outcome with the highest combined payoff for both prisoners, even if each individual may still face an incentive to defect.
8) Can this tool analyze nonstandard matrices?
Yes. You can enter any numeric payoffs, and the calculator will diagnose whether the matrix behaves like a classic prisoner dilemma or another game.