Resource allocation under uncertainty: an algebraic and qualitative treatment
This work addresses resource allocation challenges under uncertainty for domains like economics or AI, but it appears incremental as it builds on existing qualitative and algebraic methods without claiming broad breakthroughs.
The paper tackles the problem of resource allocation under uncertainty by proposing a qualitative algebraic framework using a matrix approach and binary relations to compare allocations based on social welfare. It proves the existence of maximal allocations and shows that optimal allocations can be reached through sequences of simple deals, with mechanisms introduced for discriminating among optimal allocations.
We use an algebraic viewpoint, namely a matrix framework to deal with the problem of resource allocation under uncertainty in the context of a qualitative approach. Our basic qualitative data are a plausibility relation over the resources, a hierarchical relation over the agents and of course the preference that the agents have over the resources. With this data we propose a qualitative binary relation $\unrhd$ between allocations such that $\mathcal{F}\unrhd \mathcal{G}$ has the following intended meaning: the allocation $\mathcal{F}$ produces more or equal social welfare than the allocation $\mathcal{G}$. We prove that there is a family of allocations which are maximal with respect to $\unrhd$. We prove also that there is a notion of simple deal such that optimal allocations can be reached by sequences of simple deals. Finally, we introduce some mechanism for discriminating {optimal} allocations.