Solving Game-Theoretic Differential Equations with MATLAB Implementation

This document explores methodologies for solving game-theoretic differential equations and provides detailed implementation techniques using MATLAB. Beyond fundamental solution approaches, we delve into advanced aspects including various types of differential equations and their corresponding solution strategies. The discussion encompasses MATLAB's sophisticated computational tools such as the Symbolic Math Toolbox for analytical solutions and Simulink for dynamic system modeling. Implementation aspects cover key MATLAB functions including ode45 for numerical integration of ordinary differential equations, dsolve for symbolic solutions, and optimization techniques for equilibrium point computation. Furthermore, we examine practical applications of these computational methods to real-world problems in economics and engineering domains, particularly focusing on game theory scenarios involving multiple decision-makers. The content includes code structure examples for implementing payoff function calculations and equilibrium analysis algorithms using MATLAB's mathematical programming capabilities.