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 is a powerful tool designed to analyse strategic interactions. It helps users set up different types of games, solve them, and find equilibrium points where players can no longer benefit by changing their strategies. This makes it ideal for anyone interested in exploring the complex world of game theory, whether for academic purposes or personal curiosity.

Game Types to Choose From

You can choose between two main game types: Normal Form and Extensive Form. Normal Form games use a matrix to display players' strategies and payoffs. In contrast, Extensive Form games represent strategies in a tree-like structure. This flexibility allows users to study a wide range of strategic situations.

Setting Up Your Game

When setting up a game, you’ll define the players and their strategies. The calculator allows you to specify the number of strategies available to each player. You can also select from common games like the Prisoner’s Dilemma or Stag Hunt, or you can create a custom game tailored to your needs. This feature provides versatility and ease of use.

What is Nash Equilibrium?

Nash Equilibrium is a key concept in game theory. It occurs when no player can gain by changing their strategy while others keep theirs unchanged. Here are some key points about Nash Equilibrium:

  • It reflects a stable strategy profile for all players involved.
  • Players have no incentive to deviate, as doing so wouldn’t improve their outcomes.
  • It can appear in pure or mixed strategy forms.

Exploring Dominant Strategies

A dominant strategy is one that always results in a better outcome for a player, no matter what the opponent does. This aspect is vital for players trying to optimise their decisions. Here’s why understanding dominant strategies matters:

  • They simplify decision-making for players.
  • They can lead to clear strategic advantages in competitive settings.
  • Identifying them helps in predicting opponents' actions.

Pareto Efficiency Explained

Pareto Optimality is another crucial concept in game theory. An outcome is Pareto efficient when no player can be made better off without making someone else worse off. This idea helps evaluate the fairness of outcomes in various games. Understanding this can guide players to seek solutions that benefit all participants.

Game Visualisation Features

The Game Theory Calculator also offers visualisation tools. By displaying games in matrix or tree format, it makes understanding strategies easier. Users can see potential outcomes and equilibria visually, which can enhance comprehension and analysis. This feature is particularly useful for learners and educators alike.

Applications of Game Theory

Game theory has broad applications across various fields. Its principles can be applied to economics, political Science, and even Biology. Here are a few specific areas where game theory plays a vital role:

  • Market behaviour and economic competition.
  • Conflict resolution in international relations.
  • Strategies in evolutionary biology.