Lesson 6: Computational Game Theory by Mohammad Hajiaghayi: Important Normal Form Games
In this session, we talk about important normal form games. In today's class, we continue our exploration of game theory, focusing on key concepts like utility functions, normal form games, and various types of games including common payoff games. We emphasize how utility functions can be represented numerically to reflect different preferences, making it easier to analyze decision-making in games. The class also discusses the significance of normal form games, which provide a formal representation of many real-world scenarios.
We introduced specific types of games, such as common payoff games where all players receive the same payoff for any given action profile, exemplified by the "Which Side of the Road" game. Additionally, we touched on competitive games like zero-sum games, where one player's gain is another's loss. The lecture also introduced the concept of mixed strategies, where players randomize their actions, and how these strategies relate to real-world scenarios like legal settlements.
Finally, we discussed the "P-Beauty Game," a game where participants choose numbers and win based on their proximity to the average or a fraction of the average. This game serves as an analogy for societal dynamics and decision-making processes. The class highlighted how these game theory concepts apply to real-world situations and set the stage for further discussions in upcoming sessions.
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