Game Setup
Normal-Form Game
| P2: S1 | P2: S2 | |
| P1: S1 | (a, b) | (c, d) |
| P1: S2 | (e, f) | (g, h) |
Payoff Matrix
Analysis Results
Strictly Dominant Strategies
Pure-Strategy Nash Equilibria
Game Properties
Pareto-Efficient Outcomes
Model Assumptions
- Simultaneous, one-shot game — players choose at the same time, in one round only
- Complete information — both players know the full payoff matrix
- Rational players — each player maximizes their own payoff
- Pure strategies only — no mixed-strategy equilibria computed
- 2 players, 2 strategies — 2×2 matrices only
- No binding agreements — non-cooperative game
- For educational purposes. Not financial advice. Market conventions simplified.
Understanding Game Theory
What is Game Theory?
Game theory is the study of strategic decision-making where the outcome for each participant depends on the choices of all participants. In economics, it is essential for analyzing oligopoly markets, where a small number of firms must consider competitors' actions when setting prices or output levels.
The Prisoner's Dilemma
The Prisoner's Dilemma demonstrates why individually rational choices can lead to collectively suboptimal outcomes. Each player has a strictly dominant strategy (defect), yet both would be better off cooperating. This structure appears in many economic contexts: firms in a cartel have incentives to cheat on production agreements, countries in arms races prefer to arm rather than disarm, and shared resources get overused when each user maximizes their own consumption.
Nash Equilibrium
A Nash equilibrium is an outcome where no player can improve their payoff by unilaterally changing their strategy. In this calculator, we identify pure-strategy Nash equilibria by checking whether each player's choice is a best response to the other player's choice. Some games have no pure-strategy NE but always have a mixed-strategy equilibrium (not computed here).
Dominant Strategies
A strictly dominant strategy yields a strictly higher payoff regardless of the opponent's choice. Not all games have dominant strategies. When both players have one, the outcome is determined — even if it leaves both worse off than some alternative (as in the Prisoner's Dilemma). This calculator uses strict dominance, meaning ties do not count.
Pareto Efficiency
An outcome is Pareto efficient if no other outcome can make at least one player better off without making anyone worse off. Note that Pareto-efficient outcomes are not necessarily fair or equal — an outcome where one player gets everything can still be Pareto efficient. In the Prisoner's Dilemma, three of the four outcomes are Pareto efficient; only the mutual defection (Nash equilibrium) is Pareto dominated.
Game Theory in Oligopoly (Mankiw Ch. 17)
Mankiw's Chapter 17 on oligopoly shows that firms in concentrated markets face a Prisoner's Dilemma. The monopoly outcome (low output, high prices) maximizes joint profit, but each firm has an incentive to increase production unilaterally. This tension between cooperation and self-interest drives oligopoly behavior and explains why cartels like OPEC historically struggle to maintain production agreements.
Related Topics
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only. It analyzes 2×2 normal-form games with pure strategies. Real-world strategic interactions may involve more players, more strategies, incomplete information, repeated games, and mixed strategies not captured here. For educational purposes. Not financial advice. Market conventions simplified.
