A Modified Hooke–Jeeves Algorithm in Two-Player Nonlinear Static Game: With an Application in Forest Management

Abstract

Strategy considerations for optimal outcomes play the key roles in every decision-making problems. Game theory in itself preserves the sustainability to draw some decision-making conclusions. Different forms of game exist in literature. This article is concerned with two-player nonlinear static game. We consider here the solution of the game problems through the algorithmic structures, with some modification, of Hooke–Jeeves (HJ) algorithm which is a tool to encounter unconstrained optimization. Basically, we lay emphasis on the modification of the considered function which is to be optimized. Hence, the name of the proposed algorithm is modified HJ algorithm. Numerous articles present different solutions of various real-life problems using HJ algorithm. Forest management problem is considered here under modified HJ algorithm to get solution. This article concludes with some comparative analysis with respect to some different methods, for example, analytical method and graphical method. Our proposed methodology gives better results than the results obtained in analytical method and graphical method with respect to optimal strategy sets and optimal payoff values.