Refactored Expected Value Calculations in Game Theory
- Day: 2024-12-04
- Time: 21:25 to 21:55
- Project: Dev
- Workspace: WP 2: Operational
- Status: Completed
- Priority: MEDIUM
- Assignee: Matías Nehuen Iglesias
- Tags: Game Theory, Expected Value, Python, Probability, Numerical Integration
Description
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.
Evidence
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- event_ids: []