📅 2024-12-04 — Session: Evaluated Optimal Solutions in Game Theory Scenarios
🕒 19:55–20:20
🏷️ Labels: Game Theory, Numerical Evaluation, Expected Payoff, Strategy, Optimization
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal: The session aimed to evaluate optimal strategies and expected payoffs in various game theory scenarios, focusing on numerical and symbolic methods.
Key Activities:
- Modified approaches to numerically evaluate optimal solutions after symbolic derivation, adjusting bounds and visual plots.
- Analyzed expected payoffs using custom strategies and uniform distributions.
- Developed methods for handling multiple probability density functions (PDFs) and cumulative distribution functions (CDFs) in game scenarios.
- Initiated a screening process for organizing and archiving knowledge in the Matías Automation Lab.
- Addressed errors in symbolic evaluation and numerical conversion of piecewise expressions.
- Discussed strategies for maximizing expected payoff against opponents with distinct strategies.
- Verified optimal choices in single and multi-opponent cases, focusing on risk management.
Achievements:
- Clarified and restored numerical and symbolic approaches in game theory.
- Verified the optimal choice of x = 25.25 for maximizing expected payoff in a single opponent scenario.
- Identified strategies for maximizing payoff based on opponent count.
Pending Tasks:
- Further refine numerical integration methods for handling edge cases in piecewise expressions.
- Continue exploration of strategy shifts based on opponent count and risk management.