📅 2024-12-04 — Session: Refactored Expected Value Calculations in Game Theory
🕒 21:25–21:55
🏷️ Labels: Game Theory, Expected Value, Python, Probability, Numerical Integration
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The session aimed to refine and correct the calculations of expected values and payoffs in game theory scenarios using Python.
Key Activities
- Expected Values in Game Theory: Discussed and implemented Python code to compute expected payoffs based on players’ choices.
- Correction of Expected Value Calculations: Identified and corrected errors in calculating expected values for opponents A and B, focusing on integration limits and normalization.
- Truncated Uniform Distribution: Addressed issues with calculating truncated expectations, specifically adjusting the integration limits based on variable bounds.
- Modeling Optimal Choices: Developed a framework for determining optimal choices in a three-player game, incorporating probability and optimization techniques.
- Probability Modeling Using CDFs: Modeled the probability of losing in a game using cumulative distribution functions, assuming player independence.
Achievements
- Successfully corrected expected value calculations for various scenarios, including opponents’ choices and truncated distributions.
- Implemented Python functions and plots to visualize corrected expected values and payoffs.
Pending Tasks
- Further validation of the modeling framework for optimal choices in multi-player games.
- Exploration of additional probabilistic models to enhance prediction accuracy.