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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

    Strategies and Dominance in Zero-Sum Games

    In the realm of game theory, zero-sum games are a fascinating and integral concept. These games, where one player's gain is another's loss, are a reflection of many real-world scenarios. To navigate these games effectively, understanding the strategies involved and the concept of dominance is crucial.

    Concept of Dominance in Game Theory

    Dominance is a key concept in game theory that helps players make rational decisions. In a game, a strategy is said to dominate another if it leads to at least as good an outcome in all scenarios, and a better outcome in some.

    There are two types of dominance: strict and weak. A strategy strictly dominates another if it always leads to a better outcome. On the other hand, a strategy weakly dominates another if it leads to at least as good an outcome in all scenarios, and a better outcome in at least one scenario.

    Iterative Deletion of Dominated Strategies

    Iterative deletion of dominated strategies is a common method used to simplify games in strategic form. The process involves repeatedly eliminating dominated strategies. After a dominated strategy is removed, a new game is formed, and the process is repeated until no more dominated strategies can be found. This method can help players narrow down their choices and make more informed decisions.

    Nash Equilibrium in Zero-Sum Games

    Named after the mathematician John Nash, a Nash equilibrium is a set of strategies, one for each player, such that no player can unilaterally improve their outcome by deviating from their strategy, given the other players stick to their strategies.

    In zero-sum games, the Nash equilibrium can be found where the player's strategies intersect, leading to the best possible outcome for each player considering the opponent's strategy. It's important to note that there may be more than one Nash equilibrium in a game.

    Role of Chance in Zero-Sum Games

    In some zero-sum games, chance plays a significant role. These games, known as mixed-strategy games, involve scenarios where players choose their strategies randomly, based on certain probabilities. The introduction of chance adds another layer of complexity to the game, as players must now consider not only their opponent's potential actions but also the likelihood of those actions.

    In conclusion, understanding the strategies and dominance in zero-sum games can provide a significant advantage in both the games themselves and real-life situations that mirror these games. By mastering these concepts, players can make more informed, rational decisions, leading to better outcomes.

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    Next up: Introduction to Non-Zero-Sum Games