OPTIMIZED STRATEGIES FOR OPEN-LOOP NASH EQUILIBRIUM IN DIFFERENTIAL GAMES USING THE PICARD ITERATION METHOD

Abstract

This study explores the application of the Picard iteration method to derivestrategies for open-loop Nash equilibrium (OLNE) in differential games, particularly in acompetitive market scenario involving three companies. By integrating the dynamics ofdifferential equations with game theory, this study presents a methodological approach for approximating solutions to complex strategic interactions. Through comparative analysisand visual representations, the paper introduces a novel theorem to establish essential conditions for OLNE. This work provides valuable insights into competitive strategies, dynamicsystems, and market analysis, thereby enhancing the understanding of differential games and demonstrating the effectiveness of the Picard iteration method in solving non-linear integro-differential equations within strategic frameworks.