We consider a job-shop scheduling problem with n jobs and the constraint that at most p

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\ud 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 he opponent; and 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

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In this paper we study the problem of allocating a scarce resource among several players (or agents). A central decision maker wants to maximize the total utility of all agents. However, such a solution may be unfair for one or more agents in the sense that it can be achieved through a very unbalanced allocation of the resource. On the other hand fair/balanced allocations may be far from optimal from a central point of view. So, in this paper we are interested in assessing the quality of fair solutions, i.e. in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the sum of agents utilities. This indicator is usually called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai-Smorodinski and proportional fairness.Our results are of two different types. We first formalize a number of properties holding for any general multi-agent problem without any special assumption on the agents utilities. Then we introduce an allocation problem, where each agent can consume the resource in given discrete quantities (items). In this case the maximization of the total utility is given by a Subset Sum Problem. For the resulting Fair Subset Sum Problem, in the case of two agents, we provide upper and lower bounds on the Price of Fairness as functions of an upper bound on the items size.

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