A game-theoretic model for repeated assignment problem between two selfish agents

This paper addresses a distributed system where a manager needs to assign a piece of equipment repeatedly between two selfish agents. On each day, each agent may encounter a task—routine or valuable—and can request the use of the manager's equipment to perform the task. Because the equipment benefits a valuable task more than a routine task, the manager wants to assign the equipment to a valuable task whenever possible. The two selfish agents, however, are only concerned with their own reward and do not have incentive to report their task types truthfully. To improve the system's overall performance, we design a token system such that an agent needs to spend tokens from his token bank to bid for the equipment. The two selfish agents become two players in a two–person non–zero–sum game. We find the Nash equilibrium of this game, and use numerical examples to illustrate the benefit of the token system.