In this paper, we integrate a cellular automaton model with game theory to simulate crowd evacuation from a room with consideration of obstacle removal. The room has one or more exits, one of which is blocked by obstacles. The obstacles at the exit can be removed by volunteers. We investigate the cooperative and defective behaviors of pedestrians during evacuation. The yielder game and volunteer's dilemma game are employed to resolve interpedestrian conflict. An anticipation floor field is proposed to guide the pedestrians to avoid obstacles that are being removed. We conducted experiments to determine how a variety of conditions affect overall crowd evacuation and volunteer evacuation times. The conditions were the start time of obstacle removal, number of obstacles, placement of obstacles, time spent in obstacle removal, strength of the anticipation floor field, and obstacle visibility distance. We demonstrate how reciprocity can be achieved among pedestrians and increases the efficiency of the entire evacuation process.