Summary: Hesitant fuzzy set (HFS) permits the membership function having a collection of probable values which are more effective for modelling the real-life problems. Multiple attribute decision making (MADM) process apparently assesses multiple conflicting attribute in decision making. In traditional decision making problems, each player is moving independently whereas in reality it is seen that each player aims to maximize personal profit which causes a negative impact on other player. MADM problem treats with candidate to the best alternative corresponding to the several attributes. Here, we present an MADM problem under hesitant fuzzy information and then transforming it into two-person matrix game, referred to herein as MADM game. The technique for order preference by similarity to ideal solution (TOPSIS) is one of the prominent approach for solving the MADM problems. In this work, we develop the TOPSIS based on ordered weighted aggregation (OWA) operator and hybrid hesitant fuzzy normalized Euclidean distance. Then the two approaches, namely hybrid hesitant fuzzy ordered weighted aggregation-TOPSIS (HHFOWA-TOPSIS) and the linear programming problem (LPP) are applied to solve the formulated MADM game. For solving MADM game, we apply LPP by considering the various values of \(\alpha,\psi \), and HHFOWA-TOPSIS for finding the optimal alternative according to their scores. An investment selection problem is included to explain the feasibility and superiority of our formulated approaches. A comparison analysis is drawn among the obtained results which are derived from the two approaches. LPP and HHFOWA-TOPSIS provide the best alternative for the proposed problem. Finally, conclusions about our findings and outlooks are described.