Dynamic Programming and Game-Theoretic Modeling for Resource-Constrained Decision Optimization: A Case Study of the Desert-Crossing Game

Abstract

This paper explores strategic decision-making challenges arising from a desert-crossing simulation game. Multiple scenarios are examined, including single-player settings with known or unknown weather conditions, and multi-player environments with either pre-defined or real-time strategic interactions. Dynamic programming and game-theoretic models form the foundation of the analysis. Computational techniques, such as LINGO optimization and Monte Carlo simulation, are applied to obtain and compare solutions. Under fully deterministic weather, a cyclic mining and supply-return route emerges as the optimal strategy. In stochastic environments, simplified heuristics based on expected monetary outcomes are shown to be effective. For multi-agent scenarios, integrating optimal and suboptimal routes reduces resource competition. Dynamic games further benefit from day-by-day route adjustments aimed at minimizing resource consumption while maintaining equitable returns. The study concludes with an evaluation of model performance, identifies current limitations, and outlines directions for future research.