Problem definition: Tasks sequentially arrive, and their values to the workers who are going to perform them are independent random variables. The common way to allocate tasks to workers is according to the first-in, first-out order. But this method both is inefficient and seems unfair to those who receive a low-valued task after a long wait. We are looking for a better allocation method. Academic/practical relevance: Finding a fair and efficient task allocation method is an aspiration of manpower firms that employ a pool of workers, such as salespersons, technicians, emergency medical stuff, nurses, or taxi drivers. We present many more implementations, such as turn taking and load management. Methodology: We propose a self-selected task allocation method and discuss its importance and implementations. The proposed method is defined as a cyclic queueing game with a fixed number of players. Every unit of time a prize with a random value is offered to the players according to their order in the queue, and a player who accepts a prize moves to the end of the queue. The process of choosing which prizes to accept in each position is presented as a noncooperative multiplayer game. We analyze strategies and symmetric equilibria for three variations. Results: We provide closed-form solutions and suggest a novel intuitive interpretation to find equilibria via calculating maximum-profit strategies. We complement the theoretical results by conducting a numerical study. Managerial implications: The proposed method is natural and easy to implement, its outcome is better than the common allocation by seniority, and the ratio of the expected value obtained under the two methods is unbounded.