Efficiency and Fairness of Resource Utilisation under Uncertainty

The problem of multi-agent resource allocation is important and well-studied within AI and economics. The general assumption is that the amount of each resource is known beforehand. However, many real-world problems, the exact amount of each resource may not be known at the time of decision making, e,g. in the case of weather dependent renewable energy production. This work considers a homogeneous divisible resource where the available amount is given by a probability distribution. In general, a model for efficient usage under fairness and the possibilities of manipulation is studied. Firstly, the notion of ex-ante envy-freeness, where, in expectation, agents weakly prefer their allocation over every other agent's allocation is introduced. For this case the tension between fairness and social welfare is considered. The price of envy-freeness is at least $Ømega(n), where n is the number of agents and the problem of optimising ex-ante social welfare subject to ex-ante envy-freeness is strongly NP-hard. Additionally, the possibility for an integer program to calculate the optimal ex-ante envy-free allocation for linear satiable valuation functions is presented.