We consider a task of scheduling with a common deadline on a single machine. Every player reports to a scheduler the length of his job and the scheduler needs to finish as many jobs as possible by the deadline. For this simple problem, there is a truthful mechanism that achieves maximum welfare in dominant strategies. The new aspect of our work is that in our setting players are uncertain about their own job lengths, and hence are incapable of providing truthful reports (in the strict sense of the word). For a probabilistic model for uncertainty our main results are as follows. 1) Even with relatively little uncertainty, no mechanism can guarantee a constant fraction of the maximum welfare. 2) To remedy this situation, we introduce a new measure of economic efficiency, based on a notion of a fair share of a player, and design mechanisms that are @math -fair. In addition to its intrinsic appeal, our notion of fairness implies good approximation of maximum welfare in several cases of interest. 3) In our mechanisms the machine is sometimes left idle even though there are jobs that want to use it. We show that this unfavorable aspect is unavoidable, unless one gives up other favorable aspects (e.g., give up @math -fairness). We also consider a qualitative approach to uncertainty as an alternative to the probabilistic quantitative model. In the qualitative approach we break away from solution concepts such as dominant strategies (they are no longer well defined), and instead suggest an axiomatic approach, which amounts to listing desirable properties for mechanisms. We provide a mechanism that satisfies these properties.
 This paper analyzes the problem of inducing the members of an organization to behave as if they formed a team. Considered is a conglomerate-type organization consisting of a set of semi-autonomous subunits that are coordinated by the organization's head. The head's incentive problem is to choose a set of employee compensation rules that will induce his subunit managers to communicate accurate information and take optimal decisions. The main result exhibits a particular set of compensation rules, an optimal incentive structure, that leads to team behavior. Particular attention is directed to the informational aspects of the problem. An extended example of a resource allocation model is discussed and the optimal incentive structure is interpreted in terms of prices charged by the head for resources allocated to the subunits. We consider the following problem: The Santa Claus has n presents that he wants to distribute among m kids. Each kid has an arbitrary value for each present. Let pij be the value that kid i has for present j. The Santa's goal is to distribute presents in such a way that the least lucky kid is as happy as possible, i.e he tries to maximize mini=1,...,m sumj ∈ Si pij where Si is a set of presents received by the i-th kid.Our main result is an O(log log m log log log m) approximation algorithm for the restricted assignment case of the problem when pij ∈ pj,0 (i.e. when present j has either value pj or 0 for each kid). Our algorithm is based on rounding a certain natural exponentially large linear programming relaxation usually referred to as the configuration LP. We also show that the configuration LP has an integrality gap of Ω(m1 2) in the general case, when pij can be arbitrary.