In this paper we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we characterize the set of Pareto optimal schedules in terms of size and computational complexity. We then address the problem from the single-agent point-of-view, that is we consider the problem of deciding how to submit one agent's tasks only taking into account its own objective function against the other agent, the opponent. In this regard, we consider two different settings depending on the information available to the agents: In one setting the considered agent knows in advance all information about the submission sequence of the opponent, in the second setting (as in minimax strategies in game theory) the agent has no information on the opponent strategy and wants to devise a strategy that minimizes its solution cost in the worst possible case. Finally, we assess the performance of some classical single-agent sequencing rules in the two-agent setting.
New Version and new Title on 16-06-2014.