Nowadays mobile multiplayer games have been an usual recreation, however energy-limited mobile devices confine the game running time. Noticing the component-based multiplayer game is a loosely coupled application whose components are nearly always required among players in one or more rounds, we study the collaboration of players to develop an energy-efficient offloading scheme. We formulate a 0-1 integer nonlinear programming problem to minimize the overall energy cost on player side under time-delay constraint. The problem is intractable to find the optimal solution, thus we propose a heuristic Two-phase Greedy-based Collaborative Offloading Algorithm (TGCOA) for the objective of cost minimization, while including more energy savings for low-energy players. In each round, we preferentially cache components saving more energy per data size for subsequent rounds, then preferentially offload components saving more energy for current round. Meanwhile, we always assign valid player with highest remaining energy to the uploading tasks. Simulations show that the energy cost ratios of our proposal are significantly down by 1.55% to 99.62% compared to four competing methods under different cache limitations and repeatability factors. Meanwhile, our proposal enables a 6.00% to 14.80% lower energy cost proportion for low-energy players compared to the four methods.