Ofra Amir edited subsectionWinner_Det.tex  over 9 years ago

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\item Allocating each of the agents one of their requested bundles.  \end{itemize}  However, not all candidate allocations are \emph{feasible} as some allocations consist of bundles that include the same item. For example, allocating $[\langle B,t_1\rangle,\langle A,t_2,\langle G,t_3,\langle E,t_4\rangle]$ to $a_2$ and $[\langle F,t_1\rangle,\langle D,t_2,\langle C,t_3,\langle E,t_4\rangle, \langle I,t_5\rangle]$ to $a_3$ is infeasible, as they both include \langle E,t_4\rangle. $\langle E,t_4\rangle$.  Thus, the candidate allocations need to be checked for feasibility. Finally, of all feasible allocations, the one that maximizes revenue is chosen. Agents that received bundles in the provisional allocation are termed ``happy'' while agents who did not receive any bundle are termed ``unhappy''. The winner determination problem is computationally hard~\cite{sandholm2002algorithm}. The pathfinding domain poses additional computational challenges for the winner determination process. First, the set of items is very large due to the time dimension. Second, agents have relative valuations for MDDs. Thus, if agents have unlimited budgets, they will keep bidding on all paths they bid on in previous iterations, resulting in a large number of bids and an increasing number of candidate allocations to be considered. Finally, checking whether an allocation is feasible requires solving a sub-problem of the complete pathfinding problem, namely searching for non-conflicting paths for the agents given their MDDs.