OPTIMAL STRATEGIES IN BIOECONOMIC DIFFERENTIAL GAMES: INSIGHTS FROM CHEBYSHEV TAU METHOD

Abstract

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.