Computational complexity of fair combinatorial auctions with multiple traders

Determine the computational complexity of the fair combinatorial auction that first filters batched bids using the fairness criterion derived from individual-trade bids and then selects the combination of surviving bids that maximizes the market value of the assets returned to traders, and ascertain how this complexity varies with the number of trades when there are more than two traders and more than two solvers.

Background

The paper introduces a fair combinatorial auction that combines individual-trade auctions with batched bids, where batched bids are accepted only if they improve outcomes for all traders relative to a benchmark constructed from individual-trade bids. This fairness mechanism is proposed to address indeterminacy and potential unfairness that arises in standard batch auctions, especially due to complementarities and the absence of a numeraire.

Extending the fair combinatorial auction beyond two traders and two solvers raises the winner determination problem typical of combinatorial auctions, where selecting the combination of bids that maximizes trader value can be computationally intractable. The authors suggest using fairness as a filter to discard unfair batched bids before solving the winner determination step.

The authors note that the fairness filter tightens as the number of trades increases, which may affect computational complexity. They explicitly leave the formal exploration of how the fairness filter impacts complexity, and how complexity scales with the number of trades, for future work.