📅 2024-12-04 — Session: Corrected Expected Value Calculations in Game Theory
🕒 21:25–22:00
🏷️ Labels: Game Theory, Expected Value, Python, Probability, Numerical Integration
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The objective of this session was to correct and refine the calculations of expected values in various game theory scenarios, particularly focusing on opponents’ choices and truncated uniform distributions.
Key Activities
- Calculated expected values in game scenarios using Python, addressing both winning and losing outcomes.
- Corrected expected values for opponents A and B based on their choice distributions and implications for total expected payoff.
- Identified and corrected errors in truncated expectation calculations for uniform distributions, adjusting integration limits.
- Analyzed expected values in truncated uniform distributions for variables E(A) and E(B).
- Refined expected value calculations for distributions A and B, including adjustments for low-value scenarios.
- Provided Python code and plotting instructions to visualize expected values and payoff calculations.
- Modeled optimal choices in a three-player game and analyzed the probability of losing using CDFs.
Achievements
- Successfully corrected expected value calculations for various game theory scenarios.
- Developed Python implementations for calculating and visualizing expected values and payoffs.
- Provided a structured framework for modeling optimal choices and analyzing losing probabilities in games.
Pending Tasks
- Further validation of the corrected models and implementations in diverse game scenarios.
- Exploration of more complex game theory models involving multiple players and strategies.