Week 21: Game Theory

 

Nash Equilibrium and Dominant Strategies

🔹 1. What is Game Theory?

Game Theory is the study of strategic interactions where the outcome for each participant depends on the actions of all.

  • It analyzes how players make decisions when their choices affect each other.

  • Widely used in economics, politics, business, and biology.

🔹 2. Dominant Strategy

A dominant strategy is the best choice for a player, no matter what the other players do.

  • If a player has a dominant strategy, they will always prefer it since it yields a better or equal payoff regardless of opponents' actions.

🔹 3. Nash Equilibrium

The Nash Equilibrium is a situation where no player can improve their outcome by changing their own strategy, assuming others keep theirs unchanged.

  • Each player’s strategy is optimal given the strategies of others.

  • There may be one or more Nash equilibria in a game.

  • It represents a stable state where no one benefits by unilaterally changing their choice.

🔹 4. Real-World Examples

  • Prisoner’s Dilemma: Both prisoners have dominant strategies to betray, but mutual cooperation would yield a better overall result.

  • Oligopoly pricing: Firms choose prices considering competitors’ possible reactions.

  • Traffic routing: Drivers choose routes based on expected congestion and others’ choices.

🔹 5. Why Is It Important?

  • Helps understand competitive behavior and cooperation.

  • Guides firms and policymakers in predicting outcomes.

  • Explains situations in markets, politics, and social systems where decisions depend on others.

🇹🇷 21. Hafta: Oyun Teorisi Temelleri

Nash Dengesi ve Dominant Stratejiler

🔹 1. Oyun Teorisi Nedir?

Oyun Teorisi, katılımcıların birbirlerinin kararlarını dikkate alarak stratejik etkileşimlerini inceleyen bilim dalıdır.

  • Her oyuncunun sonucu, diğerlerinin seçimlerine bağlıdır.

  • Ekonomi, siyaset, iş dünyası ve biyolojide yaygın olarak kullanılır.

🔹 2. Dominant Strateji

Dominant strateji, bir oyuncunun hangi rakip hareketi olursa olsun tercih edeceği en iyi seçenektir.

  • Bir oyuncu dominant stratejiye sahipse, her zaman onu seçer çünkü en iyi ya da eşit getiriyi sağlar.

🔹 3. Nash Dengesi

Nash Dengesi, hiçbir oyuncunun tek taraflı olarak stratejisini değiştirerek daha iyi sonuç elde edemediği durumdur.

  • Her oyuncunun seçimi, diğer oyuncuların seçimlerine göre en iyisidir.

  • Oyun içinde birden fazla Nash Dengesi olabilir.

  • Bu durum, herkesin stratejisini değiştirmeye gerek duymadığı kararlı bir dengeyi ifade eder.

🔹 4. Gerçek Hayat Örnekleri

  • Mahkûmun İkilemi: Her mahkûmun en iyi stratejisi karşısındakini ihbar etmek olsa da, işbirliği daha iyi sonuç verir.

  • Oligopol fiyatlandırması: Firmalar, rakiplerin olası fiyat kararlarını dikkate alır.

  • Trafik yönlendirme: Sürücüler, beklenen trafik yoğunluğunu ve diğer sürücülerin seçimlerini değerlendirerek rota seçer.

🔹 5. Neden Önemlidir?

  • Rekabet ve iş birliği davranışlarını anlamaya yardımcı olur.

  • Firmalar ve karar vericiler için sonuçları tahmin etmeyi sağlar.

  • Piyasalar, siyaset ve sosyal sistemlerde kararların karşılıklı bağımlılığını açıklar.

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