Lesson 5: Computational Game Theory by Mohammad Hajiaghayi: Normal Form Games
In this session, we talk about normal form games which are very important forms of games.
Last session, we discussed normal form games, building on our previous lectures on probability theory. We'll return to linear programming later, but for now, we focused on the chocolate dilemma game, where two players make decisions about taking chocolate. We explored various scenarios, such as playing against a stranger, friend, or computer, and considered how communication and repeated interactions might affect outcomes.
We also introduced the concept of repeated games, where players engage with the same opponent multiple times, leading to strategies like regret minimization. This connects to real-world situations, such as negotiating settlements, where repeated interactions can influence behavior. Additionally, we examined decision-making under risk, highlighting how people often prefer guaranteed outcomes over potentially higher but uncertain rewards, a phenomenon observed in studies by Kahneman.
Finally, we explored how these games blend mathematical models with social sciences, considering factors like variance and standard deviation alongside expected values. This interdisciplinary approach helps us understand why people might make decisions that seem irrational from a purely mathematical perspective, as social and psychological factors come into play.
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