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    Game Theory

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    • Introduction to Game Theory
      • 1.1What is Game Theory?
      • 1.2History and Importance of Game Theory
      • 1.3Understanding Basic Terminology
    • Two-Person Zero-Sum Games
      • 2.1Defining Zero-Sum Games
      • 2.2Solving Simple Zero-Sum Games
      • 2.3Strategies and Dominance in Zero-Sum Games
    • Non-Zero-Sum and Cooperative Games
      • 3.1Introduction to Non-Zero-Sum Games
      • 3.2Cooperative Games and the Core
      • 3.3Bargaining & Negotiation Techniques
    • Game Theory in Business and Economics
      • 4.1Market Analysis via Game Theory
      • 4.2Strategic Moves in Business
      • 4.3Auctions and Bidding Strategies
    • Game Theory in Politics
      • 5.1Electoral Systems and Voting Strategies
      • 5.2Power and Conflict Resolution
      • 5.3Foreign Policy and International Relations
    • Psychological Game Theory
      • 6.1Perception, Belief, and Strategic Interaction
      • 6.2Emotions and Decision-Making
      • 6.3Behavioral Biases in Strategic Thinking
    • Games of Chance and Risk
      • 7.1Probability Analysis and Risk Management
      • 7.2Gambler's Fallacy
      • 7.3Risk Tolerance and Decision Making
    • Evolutionary Game Theory
      • 8.1The Origin and Motivation for Evolutionary Game Theory
      • 8.2Evolutionary Stability Strategies
      • 8.3Application of Evolutionary Game Theory
    • Games with Sequential Moves
      • 9.1Extensive Form Representation
      • 9.2Backward Induction
      • 9.3Credible Threats and Promises
    • Game Theory in Social Interactions
      • 10.1Social Rules and Norms as Games
      • 10.2Role of Reputation and Signals
      • 10.3Social Network Analysis
    • Ethics in Game Theory
      • 11.1Fairness Concepts
      • 11.2Moral Hazards and Incentives
      • 11.3Social Dilemmas and Collective Action
    • Technological Aspects of Game Theory
      • 12.1Digital Trust and Security Games
      • 12.2AI and Machine Learning in Game Theory
      • 12.3Online Marketplaces and Digital Economy
    • Applying Game Theory in Everyday Life
      • 13.1Practical Examples of Game Theory at Work
      • 13.2Thinking Strategically in Personal Decisions
      • 13.3Final Recap and Strategizing Your Life

    Two-Person Zero-Sum Games

    Defining Zero-Sum Games

    strategy board game

    Strategy board game.

    Game theory is a fascinating field that provides a framework for understanding strategic interactions, where the outcome for each participant depends on the decisions of all. One of the most fundamental concepts in game theory is the zero-sum game.

    What is a Zero-Sum Game?

    A zero-sum game is a mathematical representation of a situation where one participant's gain or loss is exactly balanced by the losses or gains of the other participant(s). In other words, if you add up the total gains and the total losses in a zero-sum game, they will always sum to zero. This is why it's called a "zero-sum" game.

    Characteristics of Zero-Sum Games

    Zero-sum games have several defining characteristics:

    1. Two Players: While it's possible to have multi-player zero-sum games, they are most commonly played between two participants.

    2. Perfect Information: In a zero-sum game, each player has perfect knowledge of the game and the payoff for each possible combination of actions.

    3. No Cooperation: Players in a zero-sum game cannot cooperate or form alliances. Each player is out for themselves.

    4. Fixed Sum: The sum of the gains and losses of the players in a zero-sum game is always zero. If one player wins, the other must lose an equivalent amount.

    Real-Life Examples of Zero-Sum Games

    Zero-sum games are everywhere in real life. Here are a few examples:

    • Chess: In a game of chess, there can only be one winner (or the game can end in a draw). If one player wins, the other player loses. The sum of the gains and losses is zero.

    • Trading Stocks: In the short term, trading stocks can be seen as a zero-sum game. If you buy a stock and it goes up, you gain, and someone else loses. If it goes down, you lose, and someone else gains.

    • Poker: Poker is another example of a zero-sum game. The total amount of money won by some players is exactly equal to the total amount of money lost by others.

    Difference Between Zero-Sum and Non-Zero-Sum Games

    Not all games in game theory are zero-sum. In non-zero-sum games, the total gain or loss can be more or less than zero. This means that it's possible for all players to win or for all players to lose. Non-zero-sum games often involve cooperation and negotiation, and they are more representative of most real-world situations.

    In conclusion, understanding zero-sum games is crucial for understanding strategic interactions in a variety of fields, from economics to politics to sports. They provide a simple yet powerful framework for analyzing and predicting human behavior.

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