Game Theory

- May 11, 2025
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Analyse strategic interactions in game theory. Create and solve various games, find Nash equilibria, and explore different solution concepts across both normal-form and extensive-form games.

Game Setup

Payoff Matrix

Solution Concepts

Display Options

About Game Theory

Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in economics, political science, psychology, computer science, and biology.

Key Concepts
  • Nash Equilibrium: A set of strategies, one for each player, such that no player has incentive to unilaterally change their strategy.
  • Dominant Strategy: A strategy that produces a better outcome regardless of the opponent's strategy choice.
  • Pareto Optimality: An outcome where no player can be made better off without making at least one player worse off.
  • Pure vs. Mixed Strategies: Pure strategies involve deterministic choices, while mixed strategies involve probabilistic choices.
Common Games
  • Prisoner's Dilemma: Players have incentives to defect even though mutual cooperation would be better.
  • Stag Hunt: Coordination game with two equilibria, one risk-dominant and one payoff-dominant.
  • Chicken: Anti-coordination game where the worst outcome is mutual defection.
  • Battle of the Sexes: Coordination game where players prefer different outcomes but both prefer coordinating.
  • Matching Pennies: Zero-sum game with no pure strategy Nash equilibrium.
Applications

Game theory has diverse applications including:

  • Economic competition and market behaviour
  • International relations and conflict resolution
  • Evolutionary biology and animal behaviour
  • Social network formation
  • Computer science and artificial intelligence
  • Auction design and mechanism design

Understanding the Game Theory Calculator

The Game Theory calculator helps you study strategic interactions where players make decisions. It allows you to set up different types of games and solve them. You can find Nash equilibria, which are key to understanding how players can best make choices. This tool is useful for anyone interested in economics, political Science, or simply learning about strategy.

Types of Games You Can Explore

You can choose between two main types of games: normal form and extensive form. Normal form games are represented in a matrix, while extensive form games are shown as trees. Each type has its own way of demonstrating strategies and payoffs, making it easier to analyse the interactions. Here are some common games you can work with:

Setting Up Your Game

When you're ready to set up your game, the calculator offers a user-friendly interface. You can name the players and input their strategies. For normal form games, you'll create a payoff matrix by entering the strategies for both players. For extensive form games, you'll set the tree depth and branches per node, allowing for a dynamic game structure.

Finding Nash Equilibria

A key feature of the Game Theory calculator is its ability to find Nash equilibria. This is the point where neither player can benefit from changing their strategy while the Other player's strategy remains the same. The calculator will highlight these equilibria within the matrix, giving you insights into optimal strategies.

Understanding Dominant Strategies

Another important aspect the calculator covers is dominant strategies. A dominant strategy is better for a player, no matter what the other player chooses. By checking for these strategies, you can easily determine if there's a clear way for a player to win, regardless of their opponent's moves.

Exploring Pareto Optimal Outcomes

Pareto optimal outcomes are also crucial in game theory. An outcome is Pareto optimal when no player can be made better off without making another player worse off. The calculator helps you identify these outcomes, which is valuable for understanding cooperative benefits.

Visualising the Game

The Game Theory calculator includes visualisation tools to help you see the game structure clearly. You can view graphs and trees that represent the game setup and its dynamics. This visual aspect enhances your understanding and allows for a better analysis of strategies and outcomes.

Applications of Game Theory

This calculator isn't just for academics; it has real-world applications too. Game theory can be used in various areas, including:

  • Market behaviour and economic strategies
  • Conflict resolution in international relations
  • Understanding social dynamics and network formation
  • Artificial intelligence and algorithm design